Codes and association schemes : DIMACS Workshop Codes and Association Schemes, November 9-12, 1999, DIMACS Center
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書誌事項
Codes and association schemes : DIMACS Workshop Codes and Association Schemes, November 9-12, 1999, DIMACS Center
（DIMACS series in discrete mathematics and theoretical computer science, v.56）
American Mathematical Society, c2001
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注記
Includes bibliographical references
内容説明・目次
内容説明
This volume presents papers related to the DIMACS workshop, ""Codes and Association Schemes"". The articles are devoted to the following topics: applications of association schemes and of the polynomial method to properties of codes, structural results for codes, structural results for association schemes, and properties of orthogonal polynomials and their applications in combinatorics. Papers on coding theory are related to classical topics, such as perfect codes, bounds on codes, codes and combinatorial arrays, weight enumerators, and spherical designs. Papers on orthogonal polynomials provide new results on zeros and symptotic properties of standard families of polynomials encountered in coding theory. The theme of association schemes is represented by new classification results and new classes of schemes related to posets. This volume collects up-to-date applications of the theory of association schemes to coding and presents new properties of both polynomial and general association schemes. It offers a solid representation of results in problems in areas of current interest.
目次
Harmonic weight enumerators of nonbinary codes and MacWilliams identities by C. Bachoc Numerical results on the asymptotic rate of binary codes by A. Barg and D. B. Jaffe Weakly biased arrays, almost independent arrays and error-correcting codes by J. Bierbrauer and H. Schellwat Indexes of spherical codes by P. Boyvalenkov, D. Danev, and P. Kazakov Codes over $\mathbb Z_{p^n}$ and association schemes by P. Camion Bent, resilient functions and the numerical normal form by C. Carlet and P. Guillot On identifying codes by G. D. Cohen, I. Honkala, A. Lobstein, and G. Zemor Ternary Hamming and binary perfect covering codes by I. J. Dejter and K. T. Phelps A Riemann hypothesis analogue for self-dual codes by I. Duursma On perfect codes in the Johnson scheme by T. Etzion On perfect constant weight codes by T. Etzion and J. van Lint On additive $GF(4)$ codes by P. Gaborit, W. C. Huffman, J.-L. Kim, and V. Pless Integral zeroes of Krawtchouk polynomials by L. Habsieger Some algebra related to $P$- and $Q$-polynomial association schemes by T. Ito, K. Tanabe, and P. Terwilliger Bounds for the Christoffel-Darboux kernel of the binary Krawtchouk polynomials by I. Krasikov Survey of binary Krawtchouk polynomials by I. Krasikov and S. Litsyn On an algebraic method for bounding the covering radius by T. Laihonen Design systems: Combinatorial characterizations of Delsarte $\mathcal T$-designs via partially ordered sets by W. J. Martin The isomorphism problem for circulant graphs via Schur ring theory by M. Muzychuk, M. Klin, and R. Poschel New 1-generator quasi-twisted codes over GF(5) by I. Siap, N. Aydin, and D. Ray-Chaudhuri Communication complexity and orthogonal polynomials by U. Tamm Estimates of the distance distribution of nonbinary codes, with applications by A. Ashikhmin, A. Barg, and S. Litsyn.
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