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Self-Dual Codes better than the Gilbert--Varshamov bound
Alp Bassa, Henning Stichtenoth · 2017-09-21 · via cs.IT updates on arXiv.org

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

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