2022/03/29 by Bocong Chen, Guanghui Zhang, Chen, Bocong +1 · 1 citation
Computer Science · Social Sciences · Engineering · #Coding theory and cryptography #Islamic Finance and Communication #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2203.15346
The family of Goppa codes is one of the most interesting subclasses of linear codes. As the McEliece cryptosystem often chooses a random Goppa code as its key,knowledge of the number of inequivalent Goppa codes for fixed parameters may facilitate in the evaluation of the security of such a cryptosystem. In this paper we present a new approach to give an upper bound on the number of inequivalent extended irreducible binary Goppa codes. To be more specific, let n>3 be an odd prime number and q=2n; let r≥3 be a positive integer satisfying gcd(r,n)=1 and gcd(r,q(q2-1))=1. We obtain an upper bound for the number of inequivalent extended irreducible binary Goppa codes of length q+1 and degree r.