Uniqueness of codes using semidefinite programming

被引：0

作者：

Brouwer, Andries E. ^{[1
]}

Polak, Sven C. ^{[1
]}

机构：

[1] Univ Amsterdam, Korteweg De Vries Inst Math, Amsterdam, Netherlands

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2019年 / 87卷 / 08期

基金：

欧洲研究理事会;

关键词：

Code; Binary code; Uniqueness; Semidefinite programming; Golay; BOUNDS;

D O I：

10.1007/s10623-018-0589-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Forn,d,wN, letA(n,d,w) denote the maximum size of a binary code of word lengthn, minimum distanced and constant weightw. Schrijver recently showed using semidefinite programming that A(23,8,11)=1288, and the second author thatA(22,8,11)=672 andA(22,8,10)=616. Here we show uniqueness of the codes achieving these bounds. LetA(n,d) denote the maximum size of a binary code of word lengthn and minimum distanced. Gijswijt et al. showed thatA(20,8)=256. We show that there are several nonisomorphic codes achieving this bound, and classify all such codes with all distances divisible by 4.

引用

页码：1881 / 1895

页数：15

共 15 条

[1] [Anonymous], 1983, THEORY ERROR CORRECT
[2] Brouwer, 1995, HDB COMBINATORICS, P693
[3] Brouwer A.E., COMPUTER PROGRAMS
[4] Brouwer A.E, TABLES BOUNDS A N D
[5] Delsarte P., 1973, PHILIPS RES REPTS S
[6] DODUNEKOV SM, 1993, PROBL PEREDACHI INF, V29, P45
[7] Semidefinite Code Bounds Based on Quadruple Distances
Gijswijt, Dion C.
Mittelmann, Hans D.
Schrijver, Alexander
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (05) : 2697 - 2705
[8] Semidefinite bounds for nonbinary codes based on quadruples
Litjens, Bart
Polak, Sven
Schrijver, Alexander
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2017, 84 (1-2) : 87 - 100
[9] Practical graph isomorphism, II
McKay, Brendan D.
Piperno, Adolfo
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 2014, 60 : 94 - 112
[10] Nakata M., 2010, 2010 IEEE International Symposium on Computer-Aided Control System Design (CACSD) part of the IEEE Multi-Conference on Systems & Control (MSC 2010), P29, DOI 10.1109/CACSD.2010.5612693

← 1 2 →