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.
Main Authors: | , , |
---|---|
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 |
id |
doaj-9daa6bb1b3964ffe9352acf54c1d74f7 |
---|---|
record_format |
Article |
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 |