upper bounds on generalized distances we derive new asymptotic bounds for generalized distances our approach extends the classical hamming plotkin and elias bounds the latter bound involves extending the definition of generalized distances to nonlinear codes

on the dimension of subfield subcodes a new lower bound for the dimension of a subfield subcode is given this bound improves the well known lower bound of p delsarte 1975 and coincides in many cases with the true dimension of the code alternant codes and geometric goppa codes are discussed as special cases

the trace operator and redundancy of goppa codes the dimension of subfield subcodes and in particular generalized goppa codes is studied using the kernel of an associated trace map bounds on the dimension for a particular general class of binary goppa codes are obtained deeper study of some special cases and other related polynomials yields still tighter bounds for any s 1

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

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

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

splittable traffic partition in wdm sonet rings to minimize sonet adms sonet adms are the dominant cost factor in the wdm sonet rings recently several articles belvaux et al european j oper res 108 1 1998 26 35 clinescu and wan traffic partition in wdm sonet rings to minimize sonet adms submitted for publication gerstel et al proc ieee infocom 98 vol 1 pp 94 101 liu et al proc infocom vol 2 2000 pp 1020 1025 sutter et al oper res 46 5 1998 719 728 proposed a number of heuristics for traffic partition so as to use as few sonet adms as possible most of these heuristics assumes wavelength continuity i e the same wavelength is allocated on all of the links in the path established for a traffic stream it was first observed and argued by gerstel et al that the number of adms can be potentially reduced by allowing a traffic stream to be locally transferred from one adm in a wavelength to another adm in a different wavelength at any intermediate node in other words the traffic streams are splittable in this paper we study two variations of this minimum adm problem with splittable traffic streams all traffic streams have prespecified routings and all traffic streams have no prespecified routings respectively both variations are shown to be np hard for the former variation a heuristic with approximation ratio at most 5 4 is proposed for the latter variation a similar heuristic with approximation ratio 3 2 is proposed

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

improved algorithms for bipartite network flow in this paper network flow algorithms for bipartite networks are studied a network g v e is called bipartite if its vertex set v can be partitioned into two subsets v 1 and v 2 such that all edges have one endpoint in v 1 and the other in v 2 let n v n 1 v 1 n 2 v 2 m e and assume without loss of generality that n 1 leq n 2 a bipartite network is called unbalanced if n 1 ll n 2 and balanced otherwise this notion is necessarily imprecise it is shown that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks the basic idea in these improvements is a two edge push rule that allows one to charge most computation to vertices in v 1 and hence develop algorithms whose running times depend on n 1 rather than n for example it is shown that the two edge push version of goldberg and tarjan s fifo preflow push algorithm runs in o n 1 m n 1 3 time and that the analogous version of ahuja and orlin s excess scaling algorithm runs in o n 1 m n 1 2 log u time where u is the largest edge capacity these ideas are also extended to dynamic tree implementations parametric maximum flows and minimum cost flows

adaptive harmonic jammer canceler a new adaptive harmonic jammer canceler is proposed it is based on the use of two sensors that enable an adaptive generation of a reference signal that is uncorrelated with the desired signal this reference signal is used for the reconstruction of the desired signal by an adaptive subtraction method this canceler is well suited to radio communications a theoretical analysis of the convergence of the coupled algorithms is presented with the help of the associated ordinary differential equation introduced by l ljung numerical simulations illustrate the different proposed algorithms

on dantzig wolfe decomposition in integer programming and ways to perform branching in a branch and price algorithm dantzig wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound the reformulation gives rise to an integer master problem whose typically large number of variables is dealt with implicitly by using an integer programming column generation procedure also known as branch and price algorithm there is a large class of integer programs that are well suited for this solution technique in this paper we propose to base the dantzig wolfe decomposition of an integer program on the discretization of the integer polyhedron associated with a subsystem of constraints as opposed to its convexification this allows us to formulate the integrality restriction directly on the master variables and sets a theoretical framework for dealing with specific issues such as branching or the introduction of cutting planes in the master we discuss specific branching schemes and their effect on the structure of the column generation subproblem we give theoretical bounds on the complexity of the separation process and the extent of the modifications to the column generation subproblem our computational tests on the cutting stock problem and a generalisation the cutting strip problem show that in practice all fractional solutions can be eliminated using branching rules that preserve the tractability of the subproblem but there is a trade off between branching efficiency and subproblem tractability

modeling bit flipping decoding based on nonorthogonal check sums with application to iterative decoding attack of mceliece cryptosystem in this correspondence iteration 1 of bit flipping decoding based on a set of nonorthogonal check sums is analyzed for both regular and irregular models in particular the tradeoff between the hamming weight and overlapping of the check sums and the number of redundant check sums required to start converging under iterative decoding is investigated the model is then applied to an iterative attack of mceliece public key cryptosystem since a successful attack of this system can be achieved by algebraic bounded distance decoding of a random code based on this model the attack can be decomposed into two phases a preprocessing phase which for one particular key kappa consists of finding a sufficiently large set s of check sums up to a certain hamming weight and a bit flipping decoding phase which uses the set s for each message encrypted with the key kappa

the true dimension of certain binary goppa codes by applying a result from algebraic geometry due to e bombieri amer j math vol 88 p 71 105 1966 the true dimension of certain binary goppa codes is calculated the results lead in many cases to an improvement of the usual lower bound for the dimension

interbasis expansions for the isotropic 3d harmonic oscillator and bivariate krawtchouk polynomials an explicit expression for the general bivariate krawtchouk polynomials is obtained in terms of the standard krawtchouk and dual hahn polynomials the bivariate krawtchouk polynomials occur as matrix elements of the unitary reducible representations of so 3 on the energy eigenspaces of the three dimensional isotropic harmonic oscillator and the explicit formula is obtained from the decomposition of these representations into their irreducible components the decomposition entails expanding the cartesian basis states in the spherical bases that span irreducible so 3 representations the overlap coefficients are obtained from the clebsch gordan problem for the lie algebra

geometric approach to higher weights the notion of higher or generalized weights of codes is just as natural as that of the classical hamming weight the authors adopt the geometric point of view and always treat the q ary case some results and proofs being new the main goal is to present a clear picture of what is known on the subject

improving discrete model representations via symmetry considerations in this paper we focus on a useful modeling concept that is frequently ignored while formu lating discrete optimization problems very often there exists a natural symmetry inherent in the problem itself that if propagated to the model can hopelessly mire a branch and bound solver by burdening it to explore and eliminate such alternative symmetric solutions we discuss three applications where such a symmetry arises a telecommunications network design problem a noise pollution problem and a machine procurement and operation problem for each case we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability while using a popular modern day commercial branch and cut software cplex 6 5

optimal load balancing on sonet bidirectional rings in this paper we consider the ring loading problem which arises in the design of sonet bidirectional rings the issue of demand splitting divides the ring loading problem into the two kinds one allows a demand to be split and routed in two different directions and the other does not the former kind becomes a relaxation of the latter we present an efficient exact solution procedure for the case with demand splitting and a two approximation algorithm for the case without demand splitting computational results are also shown to prove the efficiency of the proposed procedures

on spectra of bch codes derives an estimate for the error term in the binomial approximation of spectra of bch codes this estimate asymptotically improves on the bounds by sidelnikov 1971 kasami et al 1985 and sole 1990

computational study of a column generation algorithm for bin packing and cutting stock problems this paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem the main focus of the research is to study the extend to which standard branch and bound enhancement features such as variable fixing the tightening of the formulation with cutting planes early branching and rounding heuristics can be usefully incorporated in a branch and price algorithm we review and compare lower bounds for the cutting stock problem we propose a pseudo polynomial heuristic we discuss the implementation of the important features of the integer programming column generation algorithm and in particular the implementation of the branching scheme our computational results demonstrate the efficiency of the resulting algorithm for various classes of bin packing and cutting stock problems

goppa codes and trace operator we study goppa codes spl gamma l g defined by the polynomial g z a z trf sub p ms f sub p s b z it is shown that the dimension of these codes never reaches the general well known bound for goppa codes new bounds are proposed depending on the value of m and p furthermore we prove that when p 2 these codes have only even weights

subclass of binary goppa codes with minimal distance equal to the design distance a subclass of binary goppa codes specified by a separable polynomial g x x sup t a and a subset l of elements of gf 2 sup m no element of l may be a root of g x and t 2 sup m 1 a is a tth power in gf 2 sup m 0 is studied for such codes it is shown that their minimal distance is equal to the design distance d 2t 1

on the dimension of trace codes an improvement of the trivial upper bound for the dimension of certain binary trace codes as well as their true dimension under certain conditions is derived the dimension of trace codes of hermitian codes is developed and the dimension of trace codes of elliptic codes is presented

the weights of the orthogonals of the extended quadratic binary goppa codes starting from results on elliptic curves and kloosterman sums over the finite field ge 2 sup t the authors determine the weights of the orthogonals of some binary linear codes the melas code of length the irreducible cyclic binary code of length 2 sup t 1 and the extended binary goppa codes defined by polynomials of degree two

least squares type algorithm for adaptive implementation of pisarenko s harmonic retrieval method pisarenko s harmonic retrieval method involves determining the minimum eigenvalue and the corresponding eigenvector of the covariance matrix of the observed random process recently thompson 9 suggested a constrained gradient search procedure for obtaining an adaptive version of pisarenko s method and his simulations have verified that the frequency estimates provided by his procedure were unbiased however the main cost of this technique was that the initial convergence rate could be very slow for certain poor initial conditions restating the constrained minimization as an unconstrained nonlinear problem we derived an alternative gauss newton type recursive algorithm which also used the second derivative matrix or hessian this algorithm may also be viewed as an approximate least squares algorithm simulations have been performed to compare this algorithm to a slight variant of thompson s original algorithm the most important conclusions are that the least squares type algorithm has faster convergence in the beginning while its convergence rate close to the true parameters depends on the signal to noise ratio of the input signal the approximate least squares algorithm resolves the sinusoids much faster than the gradient version

on the parameters of goppa codes a proof of v d goppa s 1983 lower bound to the dimension of subfield subcodes of his geometric codes is given a result on the minimum distance of these subfield subcodes is also given that generalizes the well known bound minimum distance of gamma l g or 2 deg g x 1 for classical goppa codes gamma l g over the field f sub 2 with a square free goppa polynomial g g x

a faster strongly polynomial minimum cost flow algorithm in this paper we present a new strongly polynomial time algorithm for the minimum cost flow problem based on a refinement of the edmonds karp scaling technique our algorithm solves the uncapacitated minimum cost flow problem as a sequence of on log n shortest path problems on networks with n nodes and m arcs and runs in on log nm n log n time using a standard transformation this approach yields an om log nm n log n algorithm for the capacitated minimum cost flow problem this algorithm improves the best previous strongly polynomial time algorithm due to z galil and e tardos by a factor of n2 m our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds say m is much less than m in this case the running time of the algorithm is om n log nm n log n

on the complete weight distribution of subfield subcodes of algebraic geometric codes in this paper we first study deviations of the complete weight distribution of a linear code from that of a random code then we consider a large family of subfield subcodes of algebraic geometric codes over prime fields which include bch codes and goppa codes and prove that the complete weight distribution is close to that of a random code if the code length is large compared with the genus of the curve and the degree of the divisor defining the code

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

on generalized hamming weights of bch codes introduces methods from algebraic geometry to determine generalized hamming weights of bch codes as an application of these methods the authors determine for primitive 2 resp 3 error correcting bch codes the third resp the second generalized hamming weight

chain of separable binary goppa codes and their minimal distance it is shown that subclasses of separable binary goppa codes gamma l g codes with l alpha isin gf 22l g alpha ne 0 and special goppa polynomials g x can be presented as a chain of embedded and equivalent codes the true minimal distance has been obtained for all codes of the chain

algorithms for distributing telecommunication traffic on a multiple ring sonet based network abstract we examine a problem arising in the assignment of telecommunication traffic to a set of synchronous optical network sonet rings prior sonet design algorithms determine node to ring assignments while concurrently prescribing an assignment of traffic to the rings however due to uncertain voice and data demand among client nodes it may become necessary to revise the planned routing scheme once the true values of this data are realized we develop a minimum cost flow algorithm for the case in which demands may be split across multiple rings and provide a transformation to a maximum flow problem for specially structured data the case in which each demand pair may be routed on only one ring is proven to be np hard and we accordingly provide a powerful heuristic and an effective standard valid inequality generation scheme to optimally solve this problem within reasonable computational limits the effectiveness of our approach is demonstrated on a set of randomly generated test data

convergence in distribution of lms type adaptive parameter estimates we study the asymptotic behavior of parameter estimates generated by lms least mean square adaptive estimation algorithms in stationary dependent random situations we show that subject to mild practically reasonable conditions the estimates converge in distribution further we extend this result to prove a more explicit type of convergence in distribution which explains other observed properties we then estimate the moments of this limiting distribution and discuss how this relates to the work of others

optimal placement of add drop multiplexers heuristic and exact algorithms we study a problem that has arisen recently in the design of telecommunications transmission networks at france telecom given a set of centers in a city or conglomeration linked together on a ring architecture given the expected demands between the centers and an essentially unlimited availability of rings of fixed capacity on the network assign demand pairs and corresponding add drop multiplexers to the rings so as to satisfy the demands and minimize the number of costly multiplexers installed heuristics based on simulated annealing have been developed for the basic problem and several variants france telecom is particularly interested in validating the effectiveness of the heuristics an exact algorithm based on integer column generation is shown to provide tight performance guarantees and in most cases to give provable minimum cost solutions column generation is used even though the subproblems are strongly np hard and are solved by standard mixed integer programming software in addition the master problems involve both integer columns and integer variables whereas these are 0 1 in most reported applications

cyclotomic linear codes of order 3 in this correspondence two classes of cyclotomic linear codes over gf q of order 3 are constructed and their weight distributions are determined the two classes are two weight codes and contain optimal codes they are not equivalent to irreducible cyclic codes in general when q 2

spectra of long primitive binary bch codes cannot approach the binomial distribution usually spectra weight distributions of primitive binary bch codes are supposed to approximate binomial weight distributions well for a wide range of code rates and code lengths it is shown that for any fixed code rate r 1 spectra of long n spl rarr spl infin primitive binary bch codes cannot approximate the binomial distribution at all

polynomial time attack on wild mceliece over quadratic extensions we present a polynomial time structural attack against the mceliece system based on wild goppa codes defined over a quadratic finite field extension we show that such codes can be efficiently distinguished from random codes the attack uses this property to compute a filtration that is to say a family of nested subcodes which will reveal their secret algebraic description

a transform approach to goppa codes based on a finite fourier transform of codewords over the finite field gf q m some basic properties of the class of goppa codes are presented a new lower bound on the minimum distance for these codes is derived and applied to a subclass of goppa codes which is in fact equivalent to a subset of punctured reversible cyclic codes furthermore it is shown how the class of goppa codes can be easily decoded in the context of this transformation by using the berlekamp massey decoding algorithm through a slight extension of the procedure it is also shown how this algorithm may be used m decode alternant codes up to their guaranteed error correction capability

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

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

on a question of babadi and tarokh in a series of remarkable papers babadi and tarokh proved the randomness of matrices and product of two matrices arising from binary linear block codes with respect to the empirical spectral distribution provided that their dual distances are sufficiently large however numerical experiments conducted by babadi and tarokh revealed that gold codes which have a dual distance of 5 also possess such a randomness property hence the interesting question was raised as to whether or not the stringent requirement of large dual distances can be relaxed in the theorems in order to explain the mysterious randomness of gold sequences in this paper we improve the results of babadi and tarokh on several fronts and provide an affirmative answer to this question

distributed asynchronous relaxation methods for convex network flow problems we consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment the dual of this problem is unconstrained differentiable and well suited for solution via gauss seidel relaxation we show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations are carried out in parallel by several processors in arbitrary order and with arbitrarily large interprocessor communication delays

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

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

lower bounds on the covering radius of the non binary and binary irreducible goppa codes new lower bounds on the covering radius for different subclasses of irreducible goppa codes are obtained

symmetric pseudo random matrices we consider the problem of generating symmetric pseudo random sign 1 matrices based on the similarity of their spectra to wigner s semicircular law using binary m sequences golomb sequences of lengths n 2 m 1 we give a simple explicit construction of circulant n times n sign matrices and show that their spectra converge to the semicircular law when n grows the kolmogorov complexity of the proposed matrices equals to that of golomb sequences and is at most 2 mathrm log 2 n bits

a note on hermitian codes over gf q sup 2 properties of codes defined by goppa s algebraic geometric method using hermitian curves are discussed generator and parity check matrices for such codes are derived explicitly results concerning the minimum distance and the weight distribution of the codes are provided