On the minimum length of quaternary linear codes of dimension five

被引：18

作者：

Landjev, IN

Maruta, T

机构：

[1] Bulgarian Acad Sci, Inst Math, BU-1113 Sofia, Bulgaria

[2] Aichi Prefectural Univ, Dept Informat Syst, Aichi 4801198, Japan

来源：

DISCRETE MATHEMATICS | 1999年 / 202卷 / 1-3期

关键词：

quaternary linear codes; minimum length bounds; minihypers;

D O I：

10.1016/S0012-365X(98)00354-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let n(q)(k,d) be the smallest integer n for which there exists a linear code of length n, dimension k and minimum distance d, over the q-element field. In this paper we prove the nonexistence of quaternary linear codes with parameters [190,5,141], [239,5,178], [275,5,205], [288,5,215], [291,5,217] and [488,5,365]. This gives an improved lower bound of n(4)(5,d) for d = 141,142 and determines the exact value of n(4)(5,d) for d = 178, 205, 206, 215, 217, 218, 365, 366, 367, 368. The updated table of n(4)(5,d) is also given. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：145 / 161

页数：17

共 36 条

[31] Minihypers and linear codes meeting the Griesmer bound: Improvements to results of Hamada, Helleseth and Maekawa
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[32] Multiple blocking sets in finite projective spaces and improvements to the Griesmer bound for linear codes
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[34] Characterization results on arbitrary non-weighted minihypers and on linear codes meeting the Griesmer bound
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Designs, Codes and Cryptography, 2008, 49 : 187 - 197
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[36] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\mathbb Z}_2}{{\mathbb Z}_4}}$$\end{document} -linear codes: generator matrices and duality
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Designs, Codes and Cryptography, 2010, 54 (2) : 167 - 179

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