Enumeration of irreducible and extended irreducible Goppa codes (1904.02791v1)

Abstract: We obtain upper bounds on the number of irreducible and extended irreducible Goppa codes over $GF(p)$ of length $q$ and $q+1$, respectively defined by polynomials of degree $r$, where $q=p^t$ and $r\geq 3$ is a positive integer.