3 years ago

Self-dual codes better than the Gilbert–Varshamov bound

Alp Bassa, Henning Stichtenoth

Abstract

We show that every self-orthogonal code over \({\mathbb {F}}_q\) of length n can be extended to a self-dual code, if there exists self-dual codes of length n. Using a family of Galois towers of algebraic function fields we show that over any nonprime field \({\mathbb {F}}_q\) , with \(q\ge 64\) , except possibly \(q=125\) , there are infinite families of self-dual codes, which are asymptotically better than the asymptotic Gilbert–Varshamov bound.

Open access
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