On the cyclicity of Goppa codes, parity-check subcodes of Goppa codes, and extended Goppa codes
type: Item
instance of: scholarly article
title: On the cyclicity of Goppa codes, parity-check subcodes of Goppa codes, and extended Goppa codes
zbMATH Open document ID: 0965.94025
author: Thierry P. Berger
published in: Finite Fields and their Applications
publication date: 2000-12-03T00:00:00Z
review text: Let \(K\) be an extension field of a prime finite field. A semilinear transformation on \(K^n\) is the action of a permutation of coordinates in \(K^n\) followed by an automorphism of the field \(K\). An induced-cyclic code is a code for which the cyclic property comes from a semilinear transformation. The paper contains the determination of all induced-cyclic Goppa codes. It also gives a necessary and sufficient condition for a Goppa code to have an induced-cyclic extension. Extensions of Goppa codes are shown to be alternant codes.
reviewed by: Arnaldo Garcia
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94B27
zbMATH DE Number: 1538400
zbMATH Keywords: extensions of Goppa codes
zbMATH Keywords: semilinear transformation
zbMATH Keywords: induced-cyclic Goppa codes
MaRDI profile type: Publication
full work available at URL: ffta.2000.0277
OpenAlex ID: W2078870121
cites work: Q4217874
cites work: Q4146667
cites work: Which extended Goppa codes are cyclic?
cites work: The automorphism groups of Reed-Solomon codes
DOI: 10.1006/FFTA.2000.0277
description: scientific article; zbMATH DE number 1538400