Double-error-correcting cyclic codes and absolutely irreducible polynomials over \(\text{GF}(2)\)
type: Item
instance of: scholarly article
title: Double-error-correcting cyclic codes and absolutely irreducible polynomials over \(\text{GF}(2)\)
zbMATH Open document ID: 0853.94021
author: Heeralal Janwa
author: Gary McGuire
author: Richard M. Wilson
published in: Journal of Algebra
publication date: 1996-02-04T00:00:00Z
review text: The paper studies the minimum distance of binary cyclic codes of length \(n = 2^s - 1\) with generator polynomial \(m_1 m_t (x)\) when \(m_i (x)\) is the minimal polynomial of \(\omega^i\) over \(GF(2)\) and \(\omega\) is a primitive element of \(GF (2^s)\). Using Weil's theorem and Bezout's theorem, numerical conditions are derived for the minimum distance of such a code to be greater than 4. A conjecture that would classify all such codes in terms of their minimum distance is formulated.
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 840724
zbMATH Keywords: BCH codes
zbMATH Keywords: minimum distance
zbMATH Keywords: binary cyclic codes
reviewed by: Vladimir D. Tonchev
Wikidata QID: Q106164956
MaRDI profile type: Publication
full work available at URL: jabr.1995.1372
OpenAlex ID: W2010858313
DOI: 10.1006/JABR.1995.1372
description: scientific article; zbMATH DE number 840724