Extended Irreducible Binary Sextic Goppa codes

Abstract

Let $n(>3)$ be a prime number and ${\mathbb{F}}_{2^n}$ a finite field of $2^n$ elements. Let $L={\mathbb{F}}_{2^n}\cup \{\infty \}$ be the support set and $g(x)$ an irreducible polynomial of degree $6$ over ${\mathbb{F}}_{2^n}$. In this paper, we obtain an upper bound on the number of extended irreducible binary Goppa codes $\Gamma (L,g)$ of degree $6$ and length $2^n+1$.

17 pages