Dergiler / Journal of Algebra Combinatorics Discrete Structures and Applications / 2017 / Cilt: 4 - Sayı: 3 #90791

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 $2^{n}+1$

Augustine İ. MUSUKWA, Kondwani MAGAMBA, John A. RYAN

Sayfa
235–246
DOI
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Abstract

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.