Nonexistence of some Griesmer codes over Fq

被引：7

作者：

Kumegawa, Kazuki ^{[1
]}

Maruta, Tatsuya ^{[1
]}

机构：

[1] Osaka Prefecture Univ, Dept Math & Informat Sci, Sakai, Osaka 5998531, Japan

来源：

DISCRETE MATHEMATICS | 2016年 / 339卷 / 02期

基金：

日本学术振兴会;

关键词：

Optimal linear codes; Griesmer bound; Minihyper; Arcs in PG(r; q); ARY LINEAR CODES; MINIMUM LENGTH;

D O I：

10.1016/j.disc.2015.09.030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the nonexistence of [g(q)(4, d), 4, d](q) codes ford = q(3)/2 - q(2) - 2q + 1 for q = 2(h), h >= 3, and for d = 2q(3) - 3q(2) - 2q + 1 for q >= 5, where g(q)(k, d) = Sigma(k-1)(i=0) [d/q(i)]. We also prove the nonexistence of [g(q)(k, d), k, d](q) code for d = (k - 2)q(k-1) - rq(k-2) - q + 1 for 3 <= k - 1 <= r <= q - q/p, q = p(h) with p prime. (c) 2015 Elsevier B.V. All rights reserved.

引用

页码：515 / 521

页数：7

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