Binary codes with covering radius one: Some new lower bounds

被引：7
|
作者：
Habsieger, L [1 ]
机构：
[1] UNIV BORDEAUX 1,LAB ALGORITHM ARITHMET,CNRS UMR 9936,F-33405 TALENCE,FRANCE
来源：
DISCRETE MATHEMATICS | 1997年 / 176卷 / 1-3期
关键词：
D O I：
10.1016/S0012-365X(96)00290-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study binary codes of length n with covering radius one via their characteristic functions. The covering condition is expressed as a system of linear inequalities. The excesses then have a natural interpretation that makes congruence properties clear. We present new congruences and give several improvements on the lower bounds for K(n, 1) (the minimal cardinality of such a code) given by Zhang (1991, 1992). We study more specifically the cases n = 5 mod 6 and n = 2, 4 mod 6, and get new lower bounds such as K(14, 1) greater than or equal to 1172 and K(20, 1) greater than or equal to 52 456.
引用
收藏
页码：115 / 130
页数：16
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