KRAWTCHOUK POLYNOMIALS AND UNIVERSAL BOUNDS FOR CODES AND DESIGNS IN HAMMING-SPACES

被引：82

作者：

LEVENSHTEIN, VI

机构：

[1] Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 1995年 / 41卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

LINEAR PROGRAMMING; DUALITY IN BOUNDING CODES AND ORTHOGONAL ARRAYS; OPTIMAL POLYNOMIALS; EXTREME ROOTS; SELF-DUAL CODES; CROSS-CORRELATION;

D O I：

10.1109/18.412678

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Universal bounds for the cardinality of codes in the Hamming space F-r(n) with a given minimum distance d and/or dual distance d' are stated. A self-contained proof of optimality of these bounds in the framework of the linear programming method is given. The necessary and sufficient conditions for attainability of the bounds are found. The parameters of codes satisfying these conditions are presented in Table I. As consequences, in particular, a new upper bound for the minimum distance of self-dual codes and a new lower bound for the crosscorrelation of half-linear codes are obtained.

引用

页码：1303 / 1321

页数：19

共 43 条

[31] Pless V., 1989, INTRO THEORY ERROR C, Vsecond
[32] QUIST B, 1952, ANN ACAD FENN SCI A, V134
[33] RAO CR, 1947, J ROY STAT SOC, V89, P128
[34] Schoenberg I. J., 1960, COMPOS MATH, V14, P260
[35] Semakov N. V., 1968, Problems of Information Transmission, V4, P1
[36] Semakov N.V., 1969, PROBL PEREDACHI INF, V5, P65
[37] Sidel'nikov V. M., 1980, Problems of Information Transmission, V16, P174
[38] Sidelnikov V., 1971, SOV MATH DOKL, V12, P197
[39] MAXIMUM DISTANCE Q-NARY CODES
SINGLETON, RC
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1964, 10 (02) : 116 - &
[40] Szego G, 1939, ORTHOGONAL POLYNOMIA, V23

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