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Book DetailsDIMACS - Series in Discrete Mathematics and Theoretical Computer ScienceVolume: 56; 2001; 303 ppMSC: Primary 94; 05
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.
Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published with the Association for Computer Machinery (ACM).
ReadershipGraduate students and research mathematicians interested in coding theory, algebraic combinatorics, and computer science.
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Table of Contents
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Chapters
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Harmonic weight enumerators of nonbinary codes and MacWilliams identities
-
Numerical results on the asymptotic rate of binary codes
-
Weakly biased arrays, almost independent arrays and error-correcting codes
-
Indexes of spherical codes
-
Codes over $\mathbb Z_{p^n}$ and association schemes
-
Bent, resilient functions and the numerical normal form
-
On identifying codes
-
Ternary Hamming and binary perfect covering codes
-
A Riemann hypothesis analogue for self-dual codes
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On perfect codes in the Johnson scheme
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On perfect constant weight codes
-
On additive $GF(4)$ codes
-
Integral zeroes of Krawtchouk polynomials
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Some algebra related to $P$- and $Q$-polynomial association schemes
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Bounds for the Christoffel-Darboux kernel of the binary Krawtchouk polynomials
-
Survey of binary Krawtchouk polynomials
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On an algebraic method for bounding the covering radius
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Design systems: Combinatorial characterizations of Delsarte $\mathcal T$-designs via partially ordered sets
-
The isomorphism problem for circulant graphs via Schur ring theory
-
New 1-generator quasi-twisted codes over GF(5)
-
Communication complexity and orthogonal polynomials
-
Estimates of the distance distribution of nonbinary codes, with applications
-
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
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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.
Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published with the Association for Computer Machinery (ACM).
Graduate students and research mathematicians interested in coding theory, algebraic combinatorics, and computer science.
-
Chapters
-
Harmonic weight enumerators of nonbinary codes and MacWilliams identities
-
Numerical results on the asymptotic rate of binary codes
-
Weakly biased arrays, almost independent arrays and error-correcting codes
-
Indexes of spherical codes
-
Codes over $\mathbb Z_{p^n}$ and association schemes
-
Bent, resilient functions and the numerical normal form
-
On identifying codes
-
Ternary Hamming and binary perfect covering codes
-
A Riemann hypothesis analogue for self-dual codes
-
On perfect codes in the Johnson scheme
-
On perfect constant weight codes
-
On additive $GF(4)$ codes
-
Integral zeroes of Krawtchouk polynomials
-
Some algebra related to $P$- and $Q$-polynomial association schemes
-
Bounds for the Christoffel-Darboux kernel of the binary Krawtchouk polynomials
-
Survey of binary Krawtchouk polynomials
-
On an algebraic method for bounding the covering radius
-
Design systems: Combinatorial characterizations of Delsarte $\mathcal T$-designs via partially ordered sets
-
The isomorphism problem for circulant graphs via Schur ring theory
-
New 1-generator quasi-twisted codes over GF(5)
-
Communication complexity and orthogonal polynomials
-
Estimates of the distance distribution of nonbinary codes, with applications
