Preprint A746/2014
An Improvement of the Gilbert-Varshamov Bound over Non-prime Fields
Arnaldo Garcia | Alp Bassa | Peter Beelen | Henning Stichtenoth
Keywords: towers | Galois towers | curves | finite fields | Ihara constant | Coding Theory | Gilbert-Varshamov bound

The Gilbert-Varshamov bound guarantees the existence of families of codes over the
finite field F with good asymptotic parameters. We show that this bound can be improved
for all non-prime finite fields F with at least  49 elements, except possibly for the case when F has 125 elements. We observe that the

same improvement even holds within the class of transitive codes and within the class of
self-orthogonal codes.