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.