split group codes we construct a class of codes of length n such that the minimum distance d outside of a certain subcode is up to a constant factor bounded below by the square root of n a well known property of quadratic residue codes the construction using the group algebra of an abelian group and a special partition or splitting of the group yields quadratic residue codes duadic codes and their generalizations as special cases we show that most of the special properties of these codes have analogues for split group codes and present examples of new classes of codes obtained by this construction

coping with known patterns of lies in a search game abstract in this paper we study a two person search game in which player a thinks of a real number z 0 1 and player b asks q questions of the yes no answer type to confine z to a subset r q of as small a size as possible the responses of player a to the queries of b need not all be true but the nature of lie s characterized by a set x of binary strings of length q we show that the smallest possible worst case size of r q is 2 q x and there exist algorithms for player b to achieve this we also carry out an average case analysis of the problem

duadic codes a new family of binary cyclic n n 1 2 and n n 1 2 codes are introduced which include quadratic residue qr codes when n is prime these codes are defined in terms of their idempotent generators and they exist for all odd n p 1 a 1 p 2 a 2 cdots p r a r where each p i is a prime equiv pm 1 pmod 8 dual codes are identified the minimum odd weight of a duadic n n 1 2 code satisfies a square root bound when equality holds in the sharper form of this bound vectors of minimum weight hold a projective plane the unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent 73 37 9 duadic codes all duadic codes of length less than 127 are identified and the minimum weights of their extensions are given one of the duadic codes of length 113 has greater minimum weight than the qr code of that length

polyadic constacyclic codes for any given positive integer m a necessary and sufficient condition for the existence of type i m adic constacyclic codes is given furthermore for any given integer s a necessary and sufficient condition for s to be a multiplier of a type i polyadic constacyclic code is given as an application some optimal codes from type i polyadic constacyclic codes including generalized reed solomon codes and alternant maximum distance separable codes are constructed

group testing with unreliable tests we consider the problem of locating two unknown elements x y using group testing devices assuming that up to a given number e of tests out of q can give erroneous feedback we provide optimal algorithms to search for x and y

analysis and comparison of numerical methods for the klein gordon equation in the nonrelativistic limit regime we analyze rigourously error estimates and compare numerically temporal spatial resolution of various numerical methods for solving the klein gordon kg equation in the nonrelativistic limit regime involving a small parameter 0 varepsilon ll 1 which is inversely proportional to the speed of light in this regime the solution is highly oscillating in time i e there are propagating waves with wavelength of o varepsilon 2 and o 1 in time and space respectively we begin with four frequently used finite difference time domain fdtd methods and obtain their rigorous error estimates in the nonrelativistic limit regime by paying particularly attention to how error bounds depend explicitly on mesh size h and time step as well as the small parameter varepsilon based on the error bounds in order to compute correct solutions when 0 varepsilon ll1 the four fdtd methods share the same varepsilon scalability tau o varepsilon 3 then we propose new numerical methods by using either fourier pseudospectral or finite difference approximation for spatial derivatives combined with the gautschi type exponential integrator for temporal derivatives to discretize the kg equation the new methods are unconditionally stable and their varepsilon scalability is improved to o 1 and tau o varepsilon 2 for linear and nonlinear kg equations respectively when 0 varepsilon ll1 numerical results are reported to support our error estimates

comparisons between sine gordon and perturbed nonlinear schrodinger equations for modeling light bullets beyond critical collapse abstract the sine gordon sg equation and perturbed nonlinear schrodinger nls equations are studied numerically for modeling the propagation of two space dimensional 2d localized pulses the so called light bullets in nonlinear dispersive optical media we begin with the 2 1 sg equation obtained as an asymptotic reduction in the two level dissipationless maxwell bloch system followed by the review on the perturbed nls equation in 2d for sg pulse envelopes which is globally well posed and has all the relevant higher order terms to regularize the collapse of standard critical cubic focusing nls the perturbed nls is approximated by truncating the nonlinearity into finite higher order terms undergoing focusing defocusing cycles efficient semi implicit sine pseudospectral discretizations for sg and perturbed nls are proposed with rigorous error estimates numerical comparison results between light bullet solutions of sg and perturbed nls as well as critical nls are reported which validate that the solution of the perturbed nls as well as its finite term truncations are in qualitative and quantitative agreement with the solution of sg for the light bullets propagation even after the critical collapse of cubic focusing nls in contrast standard critical nls is in qualitative agreement with sg only before its collapse as a benefit of such observations pulse propagations are studied via solving the perturbed nls truncated by reasonably many nonlinear terms which is a much cheaper task than solving sg equation directly

on the minimum distance of cyclic codes the main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds i e bch bound ht bound roos bound this bound is related to a second method for bounding the minimum distance of a cyclic code which we call shifting this method can be even stronger than the first one for all binary cyclic codes of length with two exceptions we show that our methods yield the true minimum distance the two exceptions at the end of our list are a code and its even weight subcode we treat several examples of cyclic codes of length geq 63

a gautschi type method for oscillatory second order differential equations we study a numerical method for second order differential equations in which high frequency oscillations are generated by a linear part for example semilinear wave equations are of this type the numerical scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly we prove that the method admits second order error bounds which are independent of the product of the step size with the frequencies our analysis also provides new insight into the m ollified impulse method of garcia archilla sanz serna and skeel we include results of numerical experiments with the sine gordon equation

conservation of energy momentum and actions in numerical discretizations of non linear wave equations for classes of symplectic and symmetric time stepping methods trigonometric integrators and the stormer verlet or leapfrog method applied to spectral semi discretizations of semilinear wave equations in a weakly non linear setting it is shown that energy momentum and all harmonic actions are approximately preserved over long times for the case of interest where the cfl number is not a small parameter such results are outside the reach of standard backward error analysis here they are instead obtained via a modulated fourier expansion in time

optimal strategies against a liar abstract we consider the following scenario there are two individuals say q questioner and r responder involved in a search game player r chooses a number say x from the set s 1 m player q has to find out x by asking questions of type which one of the sets a 1 a 2 a q does x belong to where the sets a 1 a q constitute a partition of s player r answers i to indicate that the number x belongs to a i we are interested in the least number of questions player q has to ask in order to be always able to correctly guess the number x provided that r can lie at most e times the case e 0 obviously reduces to the classical q ary search and the necessary number of questions is log q m the case q 2 and e 1 has been widely studied and it is generally referred to as ulam s game in this paper we consider the general case of arbitrary q 2 under the assumption that player r is allowed to lie at most twice throughout the game we determine the minimum number of questions q needs to ask in order to successfully search for x in a set of cardinality m q i for any i 1 as a corollary we obtain a counterexample to a recently proposed conjecture of aigner for the case of an arbitrary number of lies we also exactly solve the problem when player r is allowed to lie a fixed but otherwise arbitrary number of times e and m q i with i not too large with respect to q for the general case of arbitrary m we give fairly tight upper and lower bounds on the number of the necessary questions

searching with known error probability abstract we study the problem of interactive searching in a set of numbers using comparison queries under the assumption that each answer can be erroneous with a constant probability p and that a given reliability 0 2 3 o logn algorithms are given in each version of search

advanced resource connector middleware for lightweight computational grids as computational grids move away from the prototyping state reliability performance and ease of use and maintenance become focus areas of their adoption in this paper we describe arc advanced resource connector grid middleware where these issues have been given special consideration we present an in depth view of the existing components of arc and discuss some of the new components functionalities and enhancements currently under development this paper also describes architectural and technical choices that have been made to ensure scalability stability and high performance the core components of arc have already been thoroughly tested in demanding production environments where it has been in use since 2002 the main goal of this paper is to provide a first comprehensive description of arc

on the weight enumerators of duadic and quadratic residue codes in this correspondence we compute the weight enumerators of various quadratic residue codes over f sub 2 and f sub 3 together with certain codes of related families like the duadic and the quadratic double circulant codes we use a parallel algorithm to find the number of codewords of a given not too high weight from which we deduce by usual classical methods for self dual and formally self dual codes over f sub 2 and f sub 3 their associated previously unknown weight enumerators we compute weight enumerators for lengths as high as 152 for binary codes and 96 for ternary codes

lie patterns in search procedures abstract we investigate the problem of identifying an unknown set a 1 n using m queries of the form i a or more generally admitting all boolean combinations of such queries the answers need not always be true but their sequence has to follow one of the lie patterns from a prescribed set x 0 1 1 m a 1 on the i th place forces the informing source to say the truth and a 0 to lie we characterize those sets x for which the identification of a is possible and deal with the problem of the minimal size of x for which the set a can be hidden

on error bounds for the gautschi type exponential integrator applied to oscillatory second order differential equations this paper studies a numerical method for second order oscillatory differential equations in which high frequency oscillations are generated by a linear time and or solution dependent part for constant linear part it is known that the method allows second order error bounds independent of the product of the step size with the frequencies and is therefore a long time step method most real world problems are not of that kind and it is important to study more general equations the analysis in this paper shows that one obtains second order error bounds even in the case of a time and or solution dependent linear part if the matrix is evaluated at averaged positions

an exponential wave integrator sine pseudospectral method for the klein gordon zakharov system an exponential wave integrator sine pseudospectral method is presented and analyzed for discretizing the klein gordon zakharov kgz system with two dimensionless parameters 0 varepsilon le 1 and 0 gamma le 1 which are inversely proportional to the plasma frequency and the speed of sound respectively the main idea in the numerical method is to apply the sine pseudospectral discretization for spatial derivatives followed by using an exponential wave integrator for temporal derivatives in phase space the method is explicit symmetric in time and it is of spectral accuracy in space and second order accuracy in time for any fixed varepsilon varepsilon 0 and gamma gamma 0 in the mathcal o 1 plasma frequency and speed of sound regime i e varepsilon mathcal o 1 and gamma mathcal o 1 we establish rigorously error estimates for the numerical method in the energy space h 1 times l 2 we also study numerically the resolution of the method in the simultaneous high plasma fr

cyclic concatenated codes with constacyclic outer codes the known construction of cyclic concatenated codes is based on the fact that the inner is a cyclic minimal code the outer code is cyclic and the lengths of the inner and outer codes are relatively prime it is shown that if the outer code is a suitably chosen constacyclic code the overall concatenated code is always cyclic regardless of the length of the outer code moreover it follows that any cyclic code of composite length is a direct sum of cyclic concatenated codes with inner cyclic minimal codes and outer constacyclic codes this description of cyclic codes of composite length leads to the introduction of the concept of a poor code length pcl all but low rate codes of this length have a poor minimum distance a pcl is directly related to the existence of irreducible binomials in the binary case the first few pcls are 9 25 27 45 49 75 81 and 99 arbitrarily long binary cyclic codes that are better than binary bch codes of primitive length are constructed

finite difference calculus invariant structure of a class of algorithms for the nonlinear klein gordon equation in a previous work the authors have presented a formalism for deriving systematically invariant symmetric finite difference algorithms for nonlinear evolution differential equations that admit conserved quantities this formalism is herein cast in the context of exact finite difference calculus the algorithms obtained from the proposed formalism are shown to derive exactly from discrete scalar potential functions using finite difference calculus in the same sense as that of the corresponding differential equation being derivable from its associated energy function a conserved quantity a clear ramification of this result is that the derived algorithms preserve certain discrete invariant quantities which are the consistent counterpart of the invariant quantities in the continuous case results on the nonlinear stability of a class of algorithms that are derived using the proposed formalism and that preserve energy or linear momentum are discussed in the context of finite difference calculus some

energy convergence for singular limits of zakharov type systems we prove existence and uniqueness of solutions to the klein gordon zakharov system in the energy space h1 l2 on some time interval which is uniform with respect to two large parameters c and these two parameters correspond to the plasma frequency and the sound speed in the simultaneous high frequency and subsonic limit we recover the nonlinear schrodinger system at the limit we are also able to say more when we take the limits separately

sympletic finite difference approximations of the nonlinear klein gordon equation we analyze three finite difference approximations of the nonlinear klein gordon equation and show that they are directly related to symplectic mappings two of the schemes the perring skyrme and ablowitz kruskal ladik are long established and the third is a new higher order accurate scheme we test the schemes on traveling wave and periodic breather problems over long time intervals and compare their accuracy and computational costs with those of symplectic and nonsymplectic method of lines approximations and a nonsymplectic energy conserving method

computing with noisy information this paper studies the depth of noisy decision trees in which each node gives the wrong answer with some constant probability in the noisy boolean decision tree model tight bounds are given on the number of queries to input variables required to compute threshold functions the parity function and symmetric functions in the noisy comparison tree model tight bounds are given on the number of noisy comparisons for searching sorting selection and merging the paper also studies parallel selection and sorting with noisy comparisons giving tight bounds for several problems

optimal error estimates of finite difference methods for the gross pitaevskii equation with angular momentum rotation we analyze finite difference methods for the gross pitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate for the conservative crank nicolson finite difference cnfd method and semi implicit finite difference sifd method at the order of o h2 2 in the l2 norm and discrete h1 norm with time step and mesh size h besides the standard techniques of the energy method the key technique in the analysis for the sifd method is to use the mathematical induction and resp for the cnfd method is to obtain a priori bound of the numerical solution in the l norm by using the inverse inequality and the l2 norm error estimate in addition for the sifd method we also derive error bounds on the errors between the mass and energy in the discretized level and their corresponding continuous counterparts respectively which are at the same order of the convergence rate as that of the numerical solution itself finally numerical results are reported to confirm our error estimates of the numerical methods

duadic codes corresp the notion of duadic codes over gf 2 is generalized to arbitrary fields duadic codes of composite length are constructed an upper bound is given for the minimum distance of duadic codes of length a prime power