Counting extended irreducible binary Goppa codes of degree 2p and length 2^n+1

Abstract

Let $n$ and $p$ be odd primes such that $p\neq n$ and $p\nmid(2^n \pm 1)$. An upper bound on the number of inequivalent extended irreducible binary Goppa codes of degree $2p$ and length $2^{n}+1$ is produced.