Self-Dual Codes better than the Gilbert--Varshamov bound

2017/09/21 by Bassa, Alp, Stichtenoth, Henning · 1 citation
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1709.07221

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≥ 64, except possibly q=125, there are self-dual codes better than the asymptotic Gilbert--Varshamov bound.

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