  The family of Goppa codes is one of the most interesting subclasses of linear
codes. As the McEliece cryptosystem often chooses a random Goppa code as its
key,knowledge of the number of inequivalent Goppa codes for fixed parameters
may facilitate in the evaluation of the security of such a cryptosystem. In
this paper we present a new approach to give an upper bound on the number of
inequivalent extended irreducible binary Goppa codes. To be more specific, let
$n>3$ be an odd prime number and $q=2^n$; let $r\geq3$ be a positive integer
satisfying $\gcd(r,n)=1$ and $\gcd\big(r,q(q^2-1)\big)=1$. We obtain an upper
bound for the number of inequivalent extended irreducible binary Goppa codes of
length $q+1$ and degree $r$.
