On the minimum length of \(q\)-ary linear codes of dimension five
type: Item
instance of: scholarly article
title: On the minimum length of \(q\)-ary linear codes of dimension five
zbMATH Open document ID: 0926.94031
DOI: 10.1023/A:1004901203236
author: Tatsuya Maruta
published in: Geometriae Dedicata
publication date: 1999-12-02T00:00:00Z
review text: A fundamental problem in coding theory is to determine \(n_q (k,d)\), the minimum value of \(n\) for which there exists an \([n,k,d]_q\) code over \(GF(q)\) for given \(q,k\) and \(d\). A lower bound on \(n_q(k,d)\) has been provided by the well known Griesmer bound. The purpose of this paper is to determine \(n_q(5,d)\) for \[ q^4-q^3-q -\sqrt q-2<d\leq q^4-q^4+ q^2-q \text{ for all }q. \] The technique employed in determining \(n_q(5,d)\) is a geometric method.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 1036209
zbMATH Keywords: linear code
zbMATH Keywords: minihyper
zbMATH Keywords: Hamming distance
zbMATH Keywords: lower bound
zbMATH Keywords: Griesmer bound
reviewed by: Bai Kishan Dass
MaRDI profile type: Publication
full work available at URL: a:1004901203236
OpenAlex ID: W2997635840
description: scientific article; zbMATH DE number 1036209