On the number of error correcting codes

Dingding Dong, Nitya Mani, Yufei Zhao

We show that for a fixed $q$, the number of $q$-ary $t$-error correcting codes of length $n$ is at most $2^{(1+o(1))H_q(n,t)}$ for all $t \leq (1 - q^{-1})n - C_q\sqrt{n \log n}…