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 2 n − 1)) ≠ 1. Set r = p 2 or r = p 3 , we determine upper bounds on the number of inequivalent extended binary irreducible Goppa codes Γ (L , g) of degree r and length 2 n + 1 , where L = F 2 n ∪ { ∞ } is the support set and each g (x) is an irreducible polynomial of degree r over F 2 n . [ABSTRACT FROM AUTHOR]