On the minimum size of binary codes with length 2R+4 and covering radius R

被引：0

作者：

Keri, Gerzson ^{[1
]}

Oestergard, Patric R. J. ^{[2
]}

机构：

[1] Hungarian Acad Sci, Comp & Automat Res Inst, H-1111 Budapest, Hungary

[2] Aalto Univ, Dept Elect & Commun Engn, Helsinki 02015, Finland

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2008年 / 48卷 / 02期

基金：

芬兰科学院; 匈牙利科学研究基金会;

关键词：

bounds on codes; classification; covering code; covering radius;

D O I：

10.1007/s10623-007-9156-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The minimum size of a binary code with length n and covering radius R is denoted by K(n, R). For arbitrary R, the value of K(n, R) is known when n <= 2R + 3, and the corresponding optimal codes have been classified up to equivalence. By combining combinatorial and computational methods, several results for the first open case, K(2R + 4, R), are here obtained, including a proof that K(10, 3) = 12 with 11481 inequivalent optimal codes and a proof that if K(2R + 4, R) < 12 for some R then this inequality cannot be established by the existence of a corresponding self-complementary code.

引用

页码：165 / 169

页数：5

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