Interesting Examples on Maximal Irreducible Goppa Codes

Abstract

A full categorization of irreducible classical Goppa codes of degree 4 and length 9 is given: it is an interesting example in the context of finding an upper bound for the number of Goppa codes which are permutation non-equivalent and irreducible and maximal with fixed parameters q, n and r (${\mathbb F}_q$ is the field of the Goppa code, the Goppa polynomial has coefficients in ${\mathbb F}_{q^n}$ and its degree is r) using group theory techniques.