EXTREMAL SOLUTIONS OF AN INEQUALITY CONCERNING SUPPORTS OF PERMUTATION GROUPS AND PUNCTURED HADAMARD CODES

被引：0

作者：

Pongracz, Andras ^{[1
]}

机构：

[1] Univ Debrecen, Inst Math, POB 400, H-4002 Debrecen, Hungary

来源：

PUBLICACIONS MATEMATIQUES | 2022年 / 66卷 / 01期

关键词：

code; anticode; support; maximum distance; AUTOMORPHISM-GROUPS; 2-WEIGHT; FIXITY;

D O I：

10.5565/PUBLMAT6612202

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If S is the degree of a permutation group and s is the maximum degree of its elements, then S <= 2s - 2. We show that this inequality is sharp for some permutation group if and only if s is a power of 2, and then there is exactly one such permutation group up to isomorphism. The unique example is an elementary Abelian 2-group that arises from a punctured Hadamard code. Then we discuss the solutions of S = 2s - 3 and S = 2s - 4.

引用

页码：57 / 75

页数：19

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