Designs and self-dual codes with long shadows

被引：39
作者：
Bachoc, C
Gaborit, P
机构：
[1] Univ Limoges, LACO, F-87000 Limoges, France
[2] Univ Bordeaux 1, Lab A2X, F-33405 Talence, France
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2004年 / 105卷 / 01期
关键词：
self-dual codes; designs; classification; shadow;
D O I：
10.1016/j.jcta.2003.09.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we introduce the notion of s-extremal codes for self-dual binary codes and we relate this notion to the existence of 1-designs or 2-designs in these codes. We extend the classification of codes with long shadows of Elkies (Math. Res. Lett. 2(5) (1995) 643) to codes with minimum distance 6, for which we give partial classification. (C) 2003 Elsevier Inc. All rights reserved.
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页码：15 / 34
页数：20
相关论文
共 27 条
[1]  
BAARTMANS A, 2000, P 7 INT WORKSH ALG C, P51
[2]   On harmonic weight enumerators of binary codes [J].
Bachoc, C .
DESIGNS CODES AND CRYPTOGRAPHY, 1999, 18 (1-3) :11-28
[3]   An enumeration of binary self-dual codes of length 32 [J].
Bilous, RT ;
van Rees, GHJ .
DESIGNS CODES AND CRYPTOGRAPHY, 2002, 26 (1-3) :61-86
[4]  
Bosma W., 1995, HDB MAGMA FUNCTIONS
[5]   WEIGHT ENUMERATORS OF SELF-DUAL CODES [J].
BRUALDI, RA ;
PLESS, VS .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (04) :1222-1225
[6]   New extremal self-dual codes of lengths 42 and 44 [J].
Buyuklieva, S .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1997, 43 (05) :1607-1612
[7]  
Buyuklieva S., 1996, Designs, Codes and Cryptography, V9, P131, DOI 10.1023/A:1018057829391
[8]   ENUMERATION OF SELF-DUAL CODES [J].
CONWAY, JH ;
PLESS, V .
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1980, 28 (01) :26-53
[9]   A NEW UPPER BOUND ON THE MINIMAL DISTANCE OF SELF-DUAL CODES [J].
CONWAY, JH ;
SLOANE, NJA .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1990, 36 (06) :1319-1333
[10]   New extremal self-dual codes of length 62 and related extremal self-dual codes [J].
Dontcheva, R ;
Harada, M .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (07) :2060-2064
123