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

Augustine Musukwa | Zendy; Kondwani Magamba | Zendy; John A. Ryan | Zendy

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

Author(s) -

Augustine Musukwa,

Kondwani Magamba,

John A. Ryan

Publication year - 2017

Publication title -

journal of algebra combinatorics discrete structures and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.137

H-Index - 1

ISSN - 2148-838X

DOI - 10.13069/jacodesmath.327368

Subject(s) - enumeration , degree (music) , mathematics , combinatorics , integer (computer science) , binary number , prime (order theory) , upper and lower bounds , discrete mathematics , physics , arithmetic , computer science , mathematical analysis , acoustics , programming language

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.

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