On the Minimum Length of q-ary Linear Codes of Dimension Five

被引：0
作者：
TATSUYA MARUTA
机构：
[1] Aichi Prefectural Women's Junior College,
来源：
Geometriae Dedicata | 1997年 / 65卷
关键词：
linear code; the Griesmer bound; minihyper.;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$n_q \left( {k,d} \right) $$ \end{document} be the smallest integer n for which there exists a linear code of length n, dimension k and minimum Hamming distance d over the Galois field GF(q). In this paper we determine \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$n_q \left( {5,d} \right) $$ \end{document} for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$q^4 - q^3 - q - \sqrt q - 2 < d \leqslant q^4 - q^3 + q^2 - q$$ \end{document} for all q, using a geometric method.
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页码：299 / 304
页数：5
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