Extended Irreducible Binary Sextic Goppa Codes
Daitao Huang, Qin Yue · IEEE Transactions on Information Theory · 2021
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$2^{n}+1$.