Linear codes with exponentially many light vectors

被引：9
作者：
Ashikhmin, A
Barg, A
Vladut, S
机构：
[1] Bell Labs, Lucent Technol, Murray Hill, NJ 07974 USA
[2] Inst Math Luminy, UPR9016, CNRS, F-13288 Marseille 9, France
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2001年 / 96卷 / 02期
关键词：
D O I：
10.1006/jcta.2001.3206
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
G. Kalai and N. Linial (1995, IEEE Trans, Inform. Theory 41, 1467-1472) put forward the following conjecture: Let {C-n} be a sequence of binary linear codes of distance d(n) and A(dn) be the number of vectors of weight d(n) in C-n. Then log(2) A(dn) = o(n). We disprove this by constructing a family of linear codes from geometric Goppa codes in which the number of vectors of minimum weight grows exponentially with the length. (C) 2001 Academic Press.
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页码：396 / 399
页数：4
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