On the geometric constructions of optimal linear codes

被引：13

作者：

Kageyama, Yuuki ^{[1
]}

Maruta, Tatsuya ^{[1
]}

机构：

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

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2016年 / 81卷 / 03期

基金：

日本学术振兴会;

关键词：

Optimal linear codes; Griesmer; Projective geometry; Geometric puncturing; MINIMUM LENGTH; GRIESMER CODES; NONEXISTENCE; PARAMETERS;

D O I：

10.1007/s10623-015-0167-2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we generalize the construction of Griesmer codes of Belov type to construct [g(q) (k, d) + t, k, d](q) codes with an integer t > 1, where g(q) (k, d) = Sigma(i=0) (k-1) This leads to the construction of several codes of length g(q)(k, d) + 1, many of which are optimal. We also construct a q-divisible [q(2) + q, 5, q(2) - q](q) code through projective geometry. As a projective dual of the code, we construct optimal codes, giving n(q) (5, d) = g(q) (5, d) + 1 for q(4) - q(3) q(2) <= d <= (q(4) - q(3) - 2q, q >= 3, where nq(k, d) is the minimum length n for which an [n, k, dlq code exists.

引用

页码：469 / 480

页数：12

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