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

Augustine I. Musukwa, Kondwani Magamba, John A. Ryan


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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