$Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$$

Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$

Let $n$ be an odd prime and $m>1$ be a positive integer. We produce an upper bound on the number of inequivalent extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$. Some examples are given to illustrate our results.

Bibliographic Details
Main Authors:	Augustine I. Musukwa, Kondwani Magamba, John A. Ryan
Format:	Article
Language:	English
Published:	Yildiz Technical University 2017-07-01
Series:	Journal of Algebra Combinatorics Discrete Structures and Applications
Online Access:	http://jacodesmath.com/index.php/jacodesmath/article/view/138

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spelling	doaj-9daa6bb1b3964ffe9352acf54c1d74f72020-11-24T21:07:21ZengYildiz Technical UniversityJournal of Algebra Combinatorics Discrete Structures and Applications2148-838X2017-07-014390Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$Augustine I. MusukwaKondwani MagambaJohn A. RyanLet $n$ be an odd prime and $m>1$ be a positive integer. We produce an upper bound on the number of inequivalent extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$. Some examples are given to illustrate our results.http://jacodesmath.com/index.php/jacodesmath/article/view/138
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Augustine I. Musukwa Kondwani Magamba John A. Ryan
spellingShingle	Augustine I. Musukwa Kondwani Magamba John A. Ryan Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$ Journal of Algebra Combinatorics Discrete Structures and Applications
author_facet	Augustine I. Musukwa Kondwani Magamba John A. Ryan
author_sort	Augustine I. Musukwa
title	Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$
title_short	Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$
title_full	Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$
title_fullStr	Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$
title_full_unstemmed	Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$
title_sort	enumeration of extended irreducible binary goppa codes of degree $2^{m}$ and length $2^{n}+1$
publisher	Yildiz Technical University
series	Journal of Algebra Combinatorics Discrete Structures and Applications
issn	2148-838X
publishDate	2017-07-01
description	Let $n$ be an odd prime and $m>1$ be a positive integer. We produce an upper bound on the number of inequivalent extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$. Some examples are given to illustrate our results.
url	http://jacodesmath.com/index.php/jacodesmath/article/view/138
work_keys_str_mv	AT augustineimusukwa enumerationofextendedirreduciblebinarygoppacodesofdegree2mandlength2n1 AT kondwanimagamba enumerationofextendedirreduciblebinarygoppacodesofdegree2mandlength2n1 AT johnaryan enumerationofextendedirreduciblebinarygoppacodesofdegree2mandlength2n1
_version_	1716763180218187776

Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$

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