Upper bound on the number of inequivalent extended binary irreducible Goppa codes

In this paper, we always assume that p and n > 3 are two distinct odd primes, m >= 2 is a positive integer, and gcd(p(m), 2(n)(2(2n) -1)) not equal 1. Set r = p(2) or r = p(3), we determine upper bounds on the number of inequivalent extended binary irreducible Goppa codes Gamma(L, g) of degree r and length 2(n) + 1, where L = F-2n boolean OR {infinity} is the support set and each g(x) is an irreducible polynomial of degree r over F-2n.(c) 2023 Published by Elsevier B.V.