Codes derived from binary Goppa codes
type: Item
instance of: scholarly article
title: Codes derived from binary Goppa codes
zbMATH Open document ID: 0994.94034
DOI: 10.1023/A:1010406807141
published in: Problems of Information Transmission
publication date: 2002-06-03T00:00:00Z
review text: In this paper, a new family of codes based on binary Goppa codes with a special automorphism group has been constructed. The special group is such that if the coefficients of a Goppa polynomial belong to some subfield of the field \(\text{GF}(2^m)\), then the automorphism group of the code contains the group generated by the Frobenius automorphism. From the set of elements of the code that are invariant under the action of the Frobenius group, a code of smaller length, called an \(s\)-projected code, is derived. Bounds on the dimension and minimum distance for this new family of codes are obtained. Also, a polynomial-time algorithm of decoding up to the designated distance has been constructed.
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 94B35
zbMATH DE Number: 1734721
zbMATH Keywords: bounds
zbMATH Keywords: projected code
zbMATH Keywords: binary Goppa codes
zbMATH Keywords: polynomial-time algorithm
zbMATH Keywords: decoding
author: Pierre Loidreau
reviewed by: Bai Kishan Dass
MaRDI profile type: Publication
full work available at URL: a:1010406807141
OpenAlex ID: W1549692307
description: scientific article; zbMATH DE number 1734721