Uniqueness of codes using semidefinite programming

作     者：Brouwer, Andries E. Polak, Sven C. 

作者机构：Univ Amsterdam Korteweg De Vries Inst Math Amsterdam Netherlands 

出 版 物：《DESIGNS CODES AND CRYPTOGRAPHY》 (设计、编码与密码学)

年 卷 期：2019年第87卷第8期

页      面：1881-1895页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC 

主　　题：Code Binary code Uniqueness Semidefinite programming Golay 

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.