A generalisation of the Gilbert-Varshamov bound and its asymptotic evaluation

We generalize the Gilbert-Varshamov lower bound on the maximum sizeof a code with given minimum Hamming distance. By using the Delsarteinequalities, it is shown that no improvement is obtained in the asymptotic case. A further improvement is given as well; it is undecided if this improvement can beat the asymptotic Gilbert-Varshamov bound or not.