## Codes and Association Schemes: DIMACS Workshop Codes and Association Schemes, November 9-12, 1999, DIMACS CenterThis 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Numerical results on the asymptotic rate of binary codes | 25 |

Indexes of spherical codes | 47 |

Bent resilient functions and the Numerical Normal Form | 87 |

Ternary Hamming and binary perfect covering codes | 111 |

On perfect codes in the Johnson scheme | 125 |

Integral zeroes of Krawtchouk polynomials | 151 |

Some algebra related to P and Qpolynomial association schemes | 167 |

Bounds for the ChristoffelDarboux kernel of the binary Krawtchouk | 193 |

On an algebraic method for bounding the covering radius | 213 |

The isomorphism problem for circulant graphs via Schur ring theory | 241 |

New generator quasitwisted codes over GF5 | 269 |

Estimates of the distance distribution of nonbinary codes with applications | 287 |

### Other editions - View all

Codes and Association Schemes: DIMACS Workshop Codes and Association Schemes ... Alexander Barg,Simon Litsyn No preview available - 2001 |

### Common terms and phrases

1-identifying Abelian classes Abelian group Abelian scheme additive code algebra Applying arrays association scheme asymptotic basic sets bent functions bijection Cayley graphs circulant graphs code of length codewords coding theory coefficients columns combinatorial Computer Science condition conjecture construction Corollary coset covering radius cyclic group defined Definition 5.1 Delsarte denote design system distance distribution dual distance E-mail address e-perfect eigenspaces eigenvalues elements example exists finite Hamming scheme IEEE Trans integer isomorphism problem Johnson scheme Krawtchouk polynomials lattice Lemma Let f linear code Litsyn lower bound Math Mathematics matrix minimum distance modulo multiset nonzero notation obtain parameters perfect codes permutation PROOF properties PROPOSITION prove QT codes reference to Definition resp S-rings satisfies scalars Schur rings Section self-dual additive self-dual codes sequence space spherical codes Steiner system subgroup subset T-design TD pair TD system ternary Type II code upper bound vector weight enumerator zeros