The number of extended irreducible binary Goppa codes of degree (2ℓ)m and length 2n+1

Abstract

Let n and be odd prime numbers such that = n and ( , 2 n ± 1) = 1. We produce an upper bound on the number of inequivalent extended irreducible binary Goppa codes of degree (2 ) m , with m ≥ 1 and length 2 n + 1.