Preprint A742/2013
An Improvement of the Gilbert-Varshamov Bound over Non-prime Fields
Alp Bassa | Peter Beelen | Arnaldo Garcia | Henning Stichtenoth
Keywords:

The Gilbert-Varshamov bound guarantees the existence of families of codes over a
finite field K with good asymptotic parameters. We show that this bound can be improved
for all non-prime fields K with at least 49 elements, except possibly for the cardinality 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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