The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q

Xue-Bin Liang

For any positive integer $q\ge 2$ and any real number $\delta \in (0,1)$, let ${\alpha }_q(n,\delta n)$ denote the maximum size of a subset of ${\mathbb{Z}}_q^n$ with minimum Hamming distance at least $…