On the existence of cyclic and pseudo-cyclic MDS codes
type: Item
instance of: scholarly article
title: On the existence of cyclic and pseudo-cyclic MDS codes
zbMATH Open document ID: 0928.94011
DOI: 10.1006/S0195-6698(97)90000-7
author: Tatsuya Maruta
published in: European Journal of Combinatorics
publication date: 2000-01-16T00:00:00Z
review text: A linear code \(C\) of length \(n\) and dimension \(k\) over the Galois field \(\mathbb{F}_q\), denoted as an \([n,k]_q\) code, is called MDS if its minimum distance \(d\) equals \(n-k+1\). \(C\) is called pseudo-cyclic (the names semi-cyclic and constacyclic are also in use) if there exists an \(\alpha\in \mathbb{F}_q \setminus\{0\}\) such that \((c_1,\dots, c_n)\in C\) implies that \((\alpha c_n,c_2, c_2, \dots, c_{n-1})\in C\). The paper studies conditions for the existence of pseudo-cyclic codes of dimension \(k=3,4\), or 5. Existence tables are provided for \(q\leq 64\).
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 51E22
zbMATH DE Number: 1212318
zbMATH Keywords: cyclic codes
zbMATH Keywords: MDS codes
zbMATH Keywords: projective geometry
zbMATH Keywords: pseudo-cyclic codes
reviewed by: L. M. G. M. Tolhuizen
MaRDI profile type: Publication
full work available at URL: s0195-6698(97)90000-7
OpenAlex ID: W1985167474
description: scientific article; zbMATH DE number 1212318