surface crouzeix raviart element for the laplace beltrami equation in this paper we are concerned with the nonconforming finite element discretization of geometric partial differential equations we construct a surface crouzeix raviart element on the linear approximated surface analogous to a flat surface the optimal convergence theory for the new nonconforming surface finite element method is developed even though the geometric error exists by taking an intrinsic viewpoint of manifolds we introduce a new superconvergent gradient recovery method for the surface crouzeix raviart element using only the information of discretized surface the potential of serving as an asymptotically exact a posteriori error estimator is also exploited a series of benchmark numerical examples are presented to validate the theoretical results and numerically demonstrate the superconvergence of the gradient recovery method

a justesen construction of binary concatenated codes that asymptotically meet the zyablov bound for low rate an explicit construction of a sequence of binary codes that asymptotically meet the zyablov bound for rates lower than 0 30 is given by using justesen s construction of concatenation the outer codes are constructed from generalized hermitian curves these outer codes can be described without any algebraic geometry terminology while the proofs of some properties deeply rely on algebraic geometry

unconditional security from noisy quantum storage we consider the implementation of two party cryptographic primitives based on the sole assumption that no large scale reliable quantum storage is available to the cheating party we construct novel protocols for oblivious transfer and bit commitment and prove that realistic noise levels provide security even against the most general attack such unconditional results were previously only known in the so called bounded storage model which is a special case of our setting our protocols can be implemented with present day hardware used for quantum key distribution in particular no quantum storage is required for the honest parties

numerical approximation for functionals of reflecting diffusion processes the aim of this paper is to approximate the expectation of a large class of functionals of the solution x xi of a stochastic differential equation with normal reflection in a piecewise smooth domain of rd this also yields a monte carlo method for solving partial differential problems of parabolic type with mixed boundary conditions the approximation is based on a modified euler scheme for the stochastic differential equation the scheme can be driven by a sequence of bounded independently and identically distributed i i d random variables or when the domain is convex by a sequence of gaussian i i d random variables the order of weak convergence for both cases is given in the former case the order of convergence is 1 2 and it is shown to be exact by an example in the last section numerical tests are presented the behavior of the error as a function of the final time t for fixed values of the discretization step and as a function of the discretization step for fixed values of the final

a splitting step algorithm for reflected stochastic differential equations in r 1 a new algorithm which is based on the splitting step idea and the penalization method for reflected stochastic differential equation rsde in the upper half space r 1 is presented in this paper after some important estimates about rsdes and penalization odes are obtained the local pathwise error of the suggested algorithm are considered and an estimate of local error in the 2pth moment is proved under the assumptions of lipschitz continuity and linear growth some numerical experiments based on matlab programs are given to support the suggested algorithm

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

oblivious transfers and intersecting codes assume a owns t secret k bit strings she is willing to disclose one of them to b at his choosing provided he does not learn anything about the other strings conversely b does not want a to learn which secret he chose to learn a protocol for the above task is said to implement one out of t string oblivious transfer denoted sup t sub 1 ot sup k sub 2 this primitive is particularly useful in a variety of cryptographic settings an apparently simpler task corresponds to the case k 1 and t 2 of two 1 bit secrets this is known as one out of two bit oblivious transfer denoted sup 2 sub 1 ot sub 2 we address the question of implementing sup t sub 1 ot sup k sub 2 assuming the existence of a sup 2 sub 1 ot sub 2 in particular we prove that unconditionally secure sup 2 sub 1 ot sup k sub 2 can be implemented from spl theta k calls to sup 2 sub 1 ot sub 2 this is optimal up to a small multiplicative constant our solution is based on the notion of self intersecting codes of independent interest we give several efficient new constructions for such codes another contribution of this paper is a set of information theoretic definitions for correctness and privacy of unconditionally secure oblivious transfer

converses for secret key agreement and secure computing we consider information theoretic secret key sk agreement and secure function computation by multiple parties observing correlated data with access to an interactive public communication channel our main result is an upper bound on the sk length which is derived using a reduction of binary hypothesis testing to multiparty sk agreement building on this basic result we derive new converses for multiparty sk agreement furthermore we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to sk agreement finally we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data using an interactive public communication that by itself does not give away the value of the function in many cases we strengthen and improve upon previously known converse bounds our results are single shot and use only the given joint distribution of the correlated observations for the case when the correlated observations consist of independent and identically distributed in time sequences we derive strong versions of previously known converses

on the efficiency of classical and quantum secure function evaluation we provide bounds on the efficiency of secure one sided output two party computation of arbitrary finite functions from trusted distributed randomness in the statistical case from these results we derive bounds on the efficiency of protocols that use different variants of oblivious transfer ot as a black box when applied to implementations of ot these bounds generalize most known results to the statistical case our results hold in particular for transformations between a finite number of primitives and for any error in the second part we study the efficiency of quantum protocols implementing ot while most classical lower bounds for perfectly secure reductions of ot to distributed randomness still hold in the quantum setting we present a statistically secure protocol that violates these bounds by an arbitrarily large factor we then prove a weaker lower bound that does hold in the statistical quantum setting and implies that even quantum protocols cannot extend ot finally we present two lower bounds for reductions of ot to commitments and a protocol based on string commitments that is optimal with respect to both of these bounds

generalized hamming weights of linear codes the generalized hamming weight d sub r c of a binary linear code c is the size of the smallest support of any r dimensional subcode of c the parameter d sub r c determines the code s performance on the wire tap channel of type ii bounds on d sub r c and in some cases exact expressions are derived in particular a generalized griesmer bound for d sub r c is presented and examples are given of codes meeting this bound with equality

construction and decoding of a class of algebraic geometry codes a class of codes derived from algebraic plane curves is constructed the concepts and results from algebraic geometry that were used are explained in detail no further knowledge of algebraic geometry is needed parameters generator and parity check matrices are given the main result is a decoding algorithm which turns out to be a generalization of the peterson algorithm for decoding bch decoder codes

on the splitting of places in a tower of function fields meeting the drinfeld vladut bound a description of how places split in an asymptotically optimal tower of function fields studied by garcia and stichtenoth 1995 is provided and an exact count of the number of places of degree one is given this information is useful in the setting up of generator matrices for algebraic geometry codes constructed over this function field tower these long codes have performance that asymptotically improves upon the gilbert varshamov bound

vector sets for exhaustive testing of logic circuits l d universal sets are useful for exhaustively testing logic circuits with a large number of functional components designed so that every functional component depends on at most d inputs randomized and deterministic constructions of l d universal test sets are presented and lower and upper bounds on the optimal sizes of such sets are proven it is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an np complete problem

an updated table of minimum distance bounds for binary linear codes in 1973 helgert and sfinaff published a table of upper and lower bounds on the maximum minimum distance for binary linear error correcting codes up to length 127 this article presents an updated table incorporating numerous improvements that have appeared since then to simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well known general code construction techniques this program also made it possible to check the original table furthermore it offers a quick and reliable update service for future improvements

parameters of goppa codes revisited we discuss parameters of goppa 1970 codes such as minimum distance covering radius distance distribution and generalized hamming weights by a variation on the exponential sums method and combinatorial arguments we sharpen known bounds on these parameters

gaps in the binary weight distributions of reed solomon codes when a reed solomon code is expanded to form a binary code certain combinations of the spectrum of the reed solomon code and the basis used for the expansion result in large gaps in the weight distribution of the binary code it is shown that the size of these gaps can be bounded by computing the sums of various powers of the basis elements and applying a theorem normally used for cyclic codes this explains why codes obtained by using a polymomial basis often have smaller gaps in their weight distributions than those obtained by using a normal basis similar results apply to the number of intersections between codewords which can be used to show that the codewords are orthogonal

how robust is the n cube the n cube network is called faulty if it contains any faulty processor or any faulty link for any number k we want to compute the minimum number f n k of faults which is necessary for an adversary to make every n k dimensional subcube faulty reversely formulated the existence of an n k dimensional non faulty subcube can be guaranteed if there are less than f n k faults in the n cube in this paper several lower and upper bounds for f n k are derived such that the resulting gaps are small for instance if k 2 is constant then f n k q logn especially for k 2 and large n f n 2 a email protected a n 2 where a n logn 1 2 log log n 1 2 or if k w log log n then 2 k f n k 2 1 k with chosen arbitrarily small the aforementioned upper bounds are obtained by analysing the behaviour of an adversary who makes worst case distributions of a given number of faulty processors for k 2 the worst case distribution is obtained constructively in the general case the constructive methods presented in this paper lead to a rather bad upper bound which can be significantly improved by probabilistic arguments the bounds mentioned above change if the notions are relativized with respect to some given parallel fault checking procedure p in this case only subcubes which are possible outputs of p must be made faulty by the adversary the notion of directed chromatic index is defined in order to analyse the case k 2 relations between the directed chromatic index and the chromatic number are derived which are of interest in their own right

an explicit construction of a sequence of codes attaining the tsfasman vladut zink bound the first steps we present a sequence of codes attaining the tsfasman vladut zink bound the construction is based on the tower of artin schreier extensions described by garcia and stichtenoth 1995 we also determine the dual codes the first steps of the constructions are explicitly given as generator matrices

a combinatorial approach to x tolerant compaction circuits test response compaction for integrated circuits ics with scan based design for testability dft support in the presence of unknown logic values xs is investigated from a combinatorial viewpoint the theoretical foundations of x codes employed in an x tolerant compaction technique called x compact are examined through the formulation of a combinatorial model of x compact novel design techniques are developed for x codes to detect a specified maximum number of errors in the presence of a specified maximum number of unknown logic values while requiring only small fan out the special class of x codes that results leads to an avoidance problem for configurations in combinatorial designs general design methods and nonconstructive existence theorems to estimate the compaction ratio of an optimal x compactor are also derived

new upper bounds on generalized weights we derive new asymptotic upper bounds on the generalized weights of a binary linear code of a given size we also prove some asymptotic results on the distance distribution of binary codes

asymptotically optimal controls for time inhomogeneous networks a framework is introduced for the identification of controls for single class time varying queueing networks that are asymptotically optimal in the so called uniform acceleration regime a related but simpler first order or fluid control problem is first formulated for a class of performance measures that satisfy a certain continuity property it is then shown that any sequence of policies whose performances approach the infimum in the fluid control problem is asymptotically optimal for the original network problem examples of performance measures with this property are described and simulations implementing asymptotically optimal policies are presented the use of directional derivatives of the reflection map for solving fluid control problems is also illustrated this work serves to complement a large body of literature on asymptotically optimal controls for time homogeneous networks

a unified finite strain theory for membranes and ropes abstract the finite strain theory is reformulated in the frame of the tangential differential calculus tdc resulting in a unification in a threefold sense firstly ropes membranes and three dimensional continua are treated with one set of governing equations secondly the reformulated boundary value problem applies to parametrized and implicit geometries therefore the formulation is more general than classical ones as it does not rely on parametrizations implying curvilinear coordinate systems and the concept of co and contravariant base vectors this leads to the third unification tdc based models are applicable to two fundamentally different numerical approaches on the one hand one may use the classical surface fem where the geometry is discretized by curved one dimensional elements for ropes and two dimensional surface elements for membranes on the other hand it also applies to recent trace fem approaches where the geometry is immersed in a higher dimensional background mesh then the shape functions of the background mesh are evaluated on the trace of the immersed geometry and used for the approximation as such the trace fem is a fictitious domain method for partial differential equations on manifolds the numerical results show that the proposed finite strain theory yields higher order convergence rates independent of the numerical methodology the dimension of the manifold and the geometric representation type

convex duality and the skorokhod problem ii in this paper we consider skorokhod problems on polyhedral domains with a constant and possibly oblique constraint direction specified on each face of the domain and with a corresponding cone of constraint directions at the intersection of faces in part one of this paper we used convex duality to develop new methods for the construction of solutions to such skorokhod problems and for proving lipschitz continuity of the associated skorokhod maps the main alternative approach to skorokhod problems of this type is the reflection mapping technique introduced by harrison and reiman 8 in this part of the paper we apply the theory developed in part one to show that the reflection mapping technique of 8 is restricted to a slight generalization of the class of problems originally considered in 8 we further illustrate the power of the duality approach by applying it to two other classes of skorokhod problems those with normal directions of constraint and a new class that arises from a model of processor sharing in communication networks in particular we prove existence of solutions to and lipschitz continuity of the skorokhod maps associated with each of these skorokhod problems

traps for reflected brownian motion consider an open set d r d d 2 and a closed ball b d let e x tb denote the expectation of the hitting time of b for reflected brownian motion in d starting from x d we say that d is a trap domain if supx e x tb a domain d is not a trap domain if and only if the reflecting brownian motion in d is uniformly ergodic we fully characterize the simply connected planar trap domains using a geometric condition and give a number of less complete results for d 2

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

continuity of quantum conditional information we prove continuity of quantum conditional information s 12 2 with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party this can e g be used to prove the continuity of squashed entanglement

modular curves and codes with a polynomial construction in this paper we study q ary codes arising from modular curves x 0 11l over gf p 2 and some binary codes attached to them all these codes have a polynomial construction and have good asymptotic parameters for certain values of the parameters the q ary codes with q p 2 geq 49 are better than the varshamov gilbert bound and the binary codes are better than the ziablov bounds

sdes with oblique reflection on nonsmooth domains in this paper we consider stochastic differential equations with reflecting boundary conditions for domains that might have corners and for which the allowed directions of reflection at a point on the boundary of the domain are possibly oblique the main results are strong existence and uniqueness for solutions of such equations a key ingredient is a family of relatively regular functions appropriate to the given domain and directions of reflection two cases are treated in the paper in the first case the direction of reflection is single valued and varies smoothly and the main new feature is that the boundary of the domain may be nonsmooth in the second case the domain is taken to be the intersection of a finite number of domains with relatively smooth boundary and at the resulting corner points more than one oblique direction is allowed

a code decomposition approach for decoding cyclic and algebraic geometric codes an approach based on code decomposition and partial transform for constructing algorithms for decoding cyclic codes and algebraic geometric ag codes is introduced a general decoding procedure applicable to arbitrary linear codes and their subfield subcodes is then developed in particular we have developed algorithms for error and erasure decoding of cyclic codes up to their actual minimum distance error and erasure decoding of ag codes up to their designed minimum distance and decoding of subfield subcodes of ag codes geometric bch codes moreover a generalization of geometric bch codes is introduced it is shown by an example that for a simple class of ag codes the so called one point codes this generalization brings a better estimate of their minimum distance it is also shown that the algorithms developed in this paper can be applied to decode these codes up to their estimated minimum distance

on greedy algorithms in coding theory we study a wide class of problems in coding theory for which we consider two different formulations in terms of incidence matrices and in terms of hypergraphs these problems are dealt with using a greedy algorithm due to stein 1974 and lovasz 1975 some examples including constructing covering codes codes for conflict resolution separating systems source encoding with distortion etc are given a unified treatment under certain conditions derandomization can be performed leading to an essential reduction in the complexity of the constructions

probabilistic approach for nonlinear partial differential equations and stochastic partial differential equations with neumann boundary conditions abstract in this study we consider nonlinear partial differential equations pdes and stochastic pdes spdes with neumann boundary conditions on domains that satisfy the lions sznitmann saisho conditions using the convergence result based on the penalization approximation for stochastic differential equations with normal reflections on nonsmooth and nonconvex domains we establish the existence and comparison principle for the viscosity solutions of nonlinear pdes with the neumann conditions associated with the optimal control problem we also obtain for nonlinear spdes and backward spdes with neumann condition the representations of the stochastic viscosity solutions

explicit construction of optimal constant weight codes for identification via channels the identification coding theorems of r ahlswede and g dueck 1981 have shown that for any nonzero probabilities of missed and false identification it is possible to transmit exp exp nr messages with n uses of a noisy channel where r is as close as desired to the shannon capacity of the channel that capability is achieved by the identification codes explicitly constructed with a three layer concatenated constant weight code used in conjunction with a channel transmission code of rate r

sweeping by a continuous prox regular set abstract the evolution problem known as sweeping process is considered for a class of nonconvex sets called prox regular or convex assuming essentially that such sets contain in the interior a suitable subset and move continuously w r t the hausdorff distance we prove local and global existence as well as uniqueness of solutions which are continuous functions with bounded variation some examples are presented

action functional for diffusions in discontinuous media the action functional i e the rate function governing the large deviations is obtained for a family of stochastic processes with discontinuous drift and small diffusion a well known method of continuous mapping is developed which proves to be efficient in a so called stable case

an improvement of the gilbert bound for constant weight codes corresp using the goppa codes as outer codes in a construction devised by kautz and singleton an improvement of the gilbert bound for constant weight codes is obtained

on the generalized hamming weights of cyclic codes we prove several results on the generalized hamming weights ghw s of linear codes particularly for cyclic codes based on these and previously known results we give some efficient algorithms for computing ghw hierarchy of cyclic codes we give complete weight hierarchy for each of the binary cyclic codes of odd lengths spl les 31 a table of second and third ghw s of binary cyclic codes of odd lengths spl les 57 is also presented we have also computed the second ghw of all binary cyclic codes of length 63 and the third ghw of one code from each dimension

the skorohod oblique reflection problem in domains with corners and application to stochastic differential equations the skorohod oblique reflection problem for d w d a general domain in d x x d a convex cone of directions of reflection w a function ind d is considered it is first proved under a condition on d corresponding to x not being simultaneously too large and too much skewed with respect to d that given a sequence wn of functions converging in the skorohod topology tow any sequence xn n of solutions to the skorohod problem for d wn is relatively compact and any of its limit points is a solution to the skorohod problem for d w next it is shown that if d satisfies the uniform exterior sphere condition and another requirement then solutions to the skorohod problem for d w exist for everyw d d with small enough jump size the requirement is met in the case when d is piecewisecb1 is generated by continuous vector fields on the faces ofd and x makes and angle in a suitable sense of less than 2 with the cone of inward normals atd for everyx d existence of obliquely reflecting brownian motion and of weak solutions to stochastic differential equations with oblique reflection boundary conditions is derived

a stochastic differential game in the orthrant we study a zero sum stochastic differential game in the nonnegative orthrant the state of the system is governed by controlled reflecting diffusions in the nonnegative orthrant we consider discounted and average payoff evaluation criteria we prove the existence of values and optimal strategies for both payoff criteria

higher order meshing of implicit geometries part ii approximations on manifolds abstract a new concept for the higher order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher order elements is automatically generated based on level set data thereby it enables a completely automatic workflow from the geometric description to the numerical analysis without any user intervention a master level set function defines the shape of the manifold through its zero isosurface which is then restricted to a finite domain by additional level set functions it is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh the numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes

large deviations of max weight scheduling policies on convex rate regions we consider a single server discrete time system with a fixed number of users where the server picks operating points from a compact convex and coordinate convex set for this system we analyse the performance of a stabilising policy that at any given time picks operating points from the allowed rate region that maximise a weighted sum of rates where the weights depend on the work loads of the users assuming a large deviations principle ldp for the arrival processes in the skorohod space of functions that are right continuous with left hand limits we establish an ldp for the work load process using a generalised version of the contraction principle to derive the corresponding rate function with the ldp result available we then analyse the tail probabilities of the work loads under different buffering scenarios

on generic erasure correcting sets and related problems motivated by iterative decoding techniques for the binary erasure channel hollmann and tolhuizen introduced and studied the notion of generic erasure correcting sets for linear codes a generic r s erasure correcting set generates for all codes of codimension r a parity check matrix that allows iterative decoding of all correctable erasure patterns of size s or less the problem is to derive bounds on the minimum size f r s of generic erasure correcting sets and to find constructions for such sets in this paper we continue the study of these sets we derive better lower and upper bounds hollmann and tolhuizen also introduced the stronger notion of r s sets and derived bounds for their minimum size g r s here also we improve these bounds we observe that these two conceps are closely related to so called s wise intersecting codes an area in which g r s has been studied primarily with respect to ratewise performance we derive connections finally we observed that hypergraph covering can be used for both problems to derive good upper bounds

heavy traffic limits for the g h2 n m queue we establish heavy traffic stochastic process limits for queue length waiting time and overflow stochastic processes in a class ofg gi n m queueing models withn servers andm extra waiting spaces we let the arrival process be general only requiring that it satisfy a functional central limit theorem to capture the impact of the service time distribution beyond its mean within a markovian framework we consider a special class of service time distributions denoted byh2 which are mixtures of an exponential distribution with probabilityp and a unit point mass at 0 with probability 1 p these service time distributions exhibit relatively high variability having squared coefficients of variation greater than or equal to one as in halfin and whitt 1981 heavy traffic limits for queues with many exponential servers oper res 29 567 588 puhalskii and reiman 2000 the multiclassgi ph n queue in the halfin whitt regime adv appl probab 32 564 595 and garnett mandelbaum and reiman 2002 designing a call center with impatient customers manufacturing service oper management 4 208 227 we consider a sequence of queueing models indexed by the number of servers n and letn tend to infinity along with the traffic intensities nso that v n 1 n for 8 8 to treat finite waiting rooms we letm n v n for 0 8 with the specialh2 service time distribution the limit processes are one dimensional markov processes behaving like diffusion processes with different drift and diffusion functions in two different regions above and below zero we also establish a limit for theg m n m m model having exponential customer abandonments

deterministic and stochastic differential inclusions with multiple surfaces of discontinuity we consider a class of deterministic and stochastic dynamical systems with discontinuous drift f and solutions that are constrained to live in a given closed domain g in mathbb r n according to a constraint vector field d specified on the boundary partial g of the domain specifically we consider equations of the form phi theta eta u quad dot theta t in f phi t quad mbox a e t for u in an appropriate class of functions where is the constraining term in the skorokhod problem specified by g d and f is the set valued upper semicontinuous envelope of f the case g mathbb r n when there is no constraining mechanism and u is absolutely continuous corresponds to the well known setting of differential inclusions di we provide a general sufficient condition for uniqueness of solutions and lipschitz continuity of the solution map in the form of existence of a lyapunov set here we assume i g is convex and admits the representation g cup i overline c i where c i i in mathbb i is a finite collection of disjoint open convex polyhedral cones in mathbb r n each having its vertex at the origin ii f b f c is a vector field defined on g such that b assumes a constant value on each of the given cones and f c is lipschitz continuous on g and iii d is an upper semicontinuous cone valued vector field that is constant on each face of g we also provide existence results under much weaker conditions where no lyapunov set condition is imposed for stochastic differential equations sde possibly reflected that have drift coefficient f and a lipschitz continuous possibly degenerate diffusion coefficient we establish strong existence and pathwise uniqueness under appropriate conditions our approach yields new existence and uniqueness results for both di and sde even in the case g mathbb r n the work has applications in the study of scaling limits of stochastic networks

probleme de skorohod multivoque on prouve un resultat d existence et d unicite pour une generalisation par introduction d un operateur maximal monotone multivoque du probleme de skorohod avec reflexion normale deterministe associe a un convexe ferme d de r d la formulation a partir des operateurs maximaux monotones multivoques permet de considerer des drifts singuliers explosant au bord du domaine cette approche multivoque clarifie la connexion entre probleme de skorohod et semigroupes nonlineaires en guise d application on considere ensuite le cas stochastique les equations differentielles stochastiques multivoques sont ainsi revisitees par consequent cette contribution fournit une nouvelle methode de construction de diffusions reflechies normalement possedant un coefficient de derive discontinu explosif

reissner mindlin shell theory based on tangential differential calculus abstract the linear reissner mindlin shell theory is reformulated in the frame of the tangential differential calculus tdc using a global cartesian coordinate system the rotation of the normal vector is modelled with a difference vector approach the resulting equations are applicable to both explicitly and implicitly defined shells because the employed surface operators do not necessarily rely on a parametrization hence shell analysis on surfaces implied by level set functions is enabled but also the classical case of parametrized surfaces is captured as a consequence the proposed tdc based formulation is more general and may also be used in recent finite element approaches such as the tracefem and cutfem where a parametrization of the middle surface is not required herein the numerical results are obtained by isogeometric analysis using nurbs as trial and test functions for classical and new benchmark tests in the residual errors optimal higher order convergence rates are confirmed when the involved physical fields are sufficiently smooth

the skorohod oblique reflection problem in time dependent domains the deterministic skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection in the form studied here the multidimensional skorohod problem w

minimal vectors in linear codes minimal vectors in linear codes arise in numerous applications particularly in constructing decoding algorithms and studying linear secret sharing schemes however properties and structure of minimal vectors have been largely unknown we prove basic properties of minimal vectors in general linear codes then we characterize minimal vectors of a given weight and compute their number in several classes of codes including the hamming codes and second order reed muller codes further we extend the concept of minimal vectors to codes over rings and compute them for several examples turning to applications we introduce a general gradient like decoding algorithm of which minimal vectors decoding is an example the complexity of minimal vectors decoding for long codes is determined by the size of the set of minimal vectors therefore we compute this size for long randomly chosen codes another example of algorithms in this class is given by zero neighbors decoding we discuss relations between the two decoding methods in particular we show that for even codes the set of zero neighbors is strictly optimal in this class of algorithms this also implies that general asymptotic improvements of the zero neighbors algorithm in the frame of gradient like approach are impossible we also discuss a link to secret sharing schemes

a higher order finite element method for partial differential equations on surfaces a new higher order finite element method for elliptic partial differential equations on a stationary smooth surface gamma is introduced and analyzed we assume that gamma is characterized as the zero level of a level set function phi and only a finite element approximation phi h of degree k geq 1 of phi is known for the discretization of the partial differential equation finite elements of degree m geq 1 on a piecewise linear approximation of gamma are used the discretization is lifted to gamma h which denotes the zero level of phi h using a quasi orthogonal coordinate system that is constructed by applying a gradient recovery technique to phi h a complete discretization error analysis is presented in which the error is split into a geometric error a quadrature error and a finite element approximation error the main result is a h 1 gamma error bound of the form c h m h k 1 results of numerical experiments illustrate the higher order convergence of t

concatenated codes with fixed inner code and random outer code we derive lower bounds on the distance and error exponent of the coding scheme described in the title the bounds are compared to the parameters and error performance of a concatenated code family with varying inner codes of equal rates and a fixed minimum distance separable mds code as the outer code letting the inner and outer code lengths approach infinity

constant rate pcps for circuit sat with sublinear query complexity the pcp theorem arora et al 1998 arora and safra 1998 says that every np proof can be encoded to another proof namely a probabilistically checkable proof pcp which can be tested by a verifier that queries only a small part of the pcp a natural question is how large is the blow up incurred by this encoding that is how long is the pcp compared to the original np proof the state of the art work of ben sasson and sudan 2008 and dinur 2007 shows that one can encode proofs of length n by pcps of length n poly log n that can be verified using a constant number of queries in this work we show that if the query complexity is relaxed to ne then one can construct pcps of length o n for circuit sat and pcps of length o tlog t for any language in ntime t more specifically for any e 0 we present nonuniform probabilistically checkable proofs pcps of length 2o 1 e n that can be checked using ne queries for circuit sat instances of size n our pcps have perfect completeness and constant soundness this is the first constant rate pcp construction that achieves constant soundness with nontrivial query complexity o n our proof replaces the low degree polynomials in algebraic pcp constructions with tensors of transitive algebraic geometry ag codes we show that the automorphisms of an ag code can be used to simulate the role of affine transformations that are crucial in earlier high rate algebraic pcp constructions using this observation we conclude that any asymptotically good family of transitive ag codes over a constant sized alphabet leads to a family of constant rate pcps with polynomially small query complexity such codes are constructed in the appendix to this article for the first time for every message length building on an earlier construction for infinitely many message lengths by stichtenoth 2006

the threshold probability of a code we define and estimate the threshold probability spl theta of a linear code using a theorem of margulis 1974 originally conceived for the study of the probability of disconnecting a graph we then apply this concept to the study of the erasure and z channels for which we propose linear coding schemes that admit simple decoding we show that spl theta is particularly relevant to the erasure channel since linear codes achieve a vanishing error probability as long as p spl lesspl theta where p is the probability of erasure in effect spl theta can be thought of as a capacity notion designed for codes rather than for channels binomial codes haven the highest possible spl theta and achieve capacity as for the z channel a subcapacity is derived with respect to the linear coding scheme for a transition probability in the range log 3 2 1 we show how to achieve this subcapacity as a by product we obtain improved constructions and existential results for intersecting codes linear sperner families which are used in our coding schemes

the average binary weight enumerator for a class of generalized reed solomon codes an explicit weight enumerator for the set of binary expansions of a class of generalized reed solomon codes is derived this enumerator is then used to show that most of these binary codes are asymptotically good and to bound the rates of self intersecting codes

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

strongly universal hashing and identification codes via channels this article shows that spl epsiv almost strongly universal classes of hash functions can yield better explicit constructions of identification codes via channels id codes and identification plus transmission codes it codes than the previous explicit constructions of verdu and wei 1993

decoding algebraic geometric codes up to the designed minimum distance a simple decoding procedure for algebraic geometric codes c sub omega d g is presented this decoding procedure is a generalization of peterson s decoding procedure for the bch codes it can be used to correct any d 1 2 or fewer errors with complexity o n sup 3 where d is the designed minimum distance of the algebraic geometric code and n is the codelength

reflected brownian motion on an orthant we consider a k dimensional diffusion process z whose state space is the nonnegative orthant on the interior of the orthant z behaves like a kdimensional brownian motion with arbitrary covariance matrix and drift vector at each of the k 1 dimensional hyperplanes that form the boundary of the orthant z reflects instantaneously in a direction that is constant over that hyperplane there is no extant theory of multidimensional diffusion that applies to this process because the boundary of its state space is not smooth we adopt an approach that requires a restriction on the directions of reflection but reiman has shown that this restriction is met by all diffusions z arising as heavy traffic limits in open k station queuing networks our process z is defined as a path to path mapping of k dimensional brownian motion from this construction it follows that z is a continuous markov process and a semimartingale using the latter property we obtain a change of variable formula from which one can develop a complete analytical theory for the process z

second order weight distributions a fundamental property of codes the second order weight distribution is proposed to solve the problems such as computing second moments of weight distributions of linear code ensembles a series of results parallel to those for weight distributions is established for second order weight distributions in particular an analogue of macwilliams identities is proved the second order weight distributions of regular ldpc code ensembles are then computed as easy consequences the second moments of weight distributions of regular ldpc code ensembles are obtained furthermore the application of second order weight distributions in random coding approach is discussed the second order weight distributions of the ensembles generated by a so called 2 good random generator or parity check matrix are computed where a 2 good random matrix is a kind of generalization of the uniformly distributed random matrix over a finite filed and is very useful for solving problems that involve pairwise or triple wise properties of sequences it is shown that the 2 good property is reflected in the second order weight distribution which thus plays a fundamental role in some well known problems in coding theory and combinatorics an example of linear intersecting codes is finally provided to illustrate this fact

performance of quantizers on noisy channels using structured families of codes achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers it is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end to end distortion decays to zero exponentially fast as a function of the overall transmission rate and is achieved by choosing a channel code rate that is independent of the overall transmission rate we show that for certain families of practical channel codes and binary lattice vector quantizers the overall distortion can be made to decay to zero exponentially fast as a function of the square root of transmission rate this is achieved by carefully choosing a channel code rate that decays to zero as the transmission rate grows explicit channel code rate schedules are obtained for several well known families of channel codes

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

a 55 16 19 binary goppa code corresp a 55 16 19 binary goppa code and some related codes are described these codes are found to contain more codewords than any previously known codes of the same length and minimum distance

generalized bsdes and nonlinear neumann boundary value problems we study a new class of backward stochastic differential equations which involves the integral with respect to a continuous increasing process this allows us to give a probabilistic formula for solutions of semilinear partial differential equations with neumann boundary condition where the boundary condition itself is nonlinear we consider both parabolic and elliptic equations

generalized reed solomon codes from algebraic geometry a few years ago tsfasman em et al using results from algebraic geometry showed that there is a sequence of codes which are generalizations of goppa codes and which exceed the gilbert varshamov bound we show that a similar sequence of codes in fact the duals of the previous codes can be found by generalizing the construction of reed solomon codes our approach has the advantage that it uses less complicated concepts from algebraic geometry

source and channel rate allocation for channel codes satisfying the gilbert varshamov or tsfasman vladut zink bounds we derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the gilbert varshamov or tsfasman vladut zink 1984 bounds formulas giving the high resolution vector quantizer distortion of these systems are also derived in addition we give bounds on how far below the channel capacity the transmission rate should be for a given delay constraint the bounds obtained depend on the relationship between channel code rate and relative minimum distance guaranteed by the gilbert varshamov bound and do not require sophisticated decoding beyond the error correction limit we demonstrate that the end to end mean squared error decays exponentially fast as a function of the overall transmission rate which need not be the case for certain well known structured codes such as hamming codes

intersecting goppa codes bounds on the rates of intersecting goppa codes are derived and compared with previous bounds on intersecting codes intersecting self intersecting and highly intersecting goppa codes are discussed in detail it is shown that asymptotically good intersecting goppa codes exist and lower bounds are given on their rates six theorems for goppa codes are also presented

a multidimensional process involving local time on presente une approche probabiliste a un probleme pose par mckean 1967 pour la construction d un systeme de n particules sur r avec un generateur formel

polynomial time construction of codes ii spherical codes and the kissing number of spheres a spherical code is a finite set x of points lying on the unit sphere of r sup n for such a set we define spl rho x as the minimum of the squared distances spl par x y spl par sup 2 when x y spl isin x and x spl ne y define r spl rho lim sup n spl rarr spl infin spl rho x p log sub 2 cardx n chabauty in 1953 and shannon in 1959 have given a lower bound for r spl rho namely r spl rho r sub cs spl rho 1 1 3log sub 2 spl rho 4 p the complexity of construction of the spherical codes used in order to get this bound is doubly exponential the polynomially constructible spherical bound r sub pol spl rho is defined as above with the additional restriction that only families of codes with polynomial complexity of construction are considered we prove r sub pol spl rho spl ges r sub cs spl rho 2 if spl rho spl les 1 535 denote by spl tau sub x n the number of spheres of equal radius that touch one sphere in the n dimensional space given by some explicit family x that is a family of arrangements of spheres the asymptotic polynomially constructible kissing number is spl theta sub pol lim sup log sub 2 spl tau sub x n n when x ranges over all polynomially constructible families we prove spl theta sub pol spl ges 2 15 0 133 spl middot spl middot spl middot

intersecting codes and independent families a binary intersecting code is a linear code with the property that any two nonzero codewords have intersecting supports these codes appear in a wide variety of contexts and applications e g multiple access cryptography and information theory this paper is devoted partly to the study of intersecting codes and partly to their use in constructing large t independent families of binary vectors the latter subject has by now been extensively studied and has application in vlsi testing defect correction e biased probability spaces and derandomization by concatenation methods we construct codes with the highest known fate asymptotically we then generalize the concept to t wise intersecting codes we give bounds on the achievable rate of such codes both existential and constructive we show how t wise intersecting codes can be used to obtain t 1 independent families with this method we obtain improved asymptotical constructions of t independent families complexity issues are discussed

distance properties of expander codes the minimum distance of some families of expander codes is studied as well as some related families of codes defined on bipartite graphs the weight spectrum and the minimum distance of a random ensemble of such codes are computed and it is shown that it sometimes meets the gilbert varshamov gv bound a lower bound on the minimum distances of constructive families of expander codes is derived the relative minimum distance of the expander code is shown to exceed the product bound i e the quantity spl delta sub 0 spl delta sub 1 where spl delta sub 0 and spl delta sub 1 are the minimum relative distances of the constituent codes as a consequence of this a polynomially constructible family of expander codes is obtained whose relative distance exceeds the zyablov bound on the distance of serial concatenations

a combinatorial approach to deriving lower bounds for perfectly secure oblivious transfer reductions consider the scenario where we are given an ideal functionality of oblivious transfer ot and we wish to construct a larger ot by invoking the above functionality as a black box how many invocations of an ideal ot functionality are necessary in tackling this problem some lower bounds were derived using entropy previously in this paper we manage to achieve tighter lower bounds by employing a combinatorial approach this new approach yields lower bounds which are two times larger than the existing bounds