An improvement of the Gilbert-Varshamov bound over nonprime fields
Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2014) An improvement of the Gilbert-Varshamov bound over nonprime fields. IEEE Transactions on Information Theory, 60 (7). pp. 3859-3861. ISSN 0018-9448
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Official URL: http://dx.doi.org/10.1109/TIT.2014.2316531
The Gilbert-Varshamov bound guarantees the existence of families of codes over the finite field Fℓ with good asymptotic parameters. We show that this bound can be improved for all nonprime fields Fℓ with ℓ ≥ 49 , except possibly ℓ = 125. We observe that the same improvement even holds within the class of transitive codes and within the class of self-orthogonal codes.
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