Beating the probabilistic lower bound on $q$-perfect hashing

Chaoping Xing, Chen Yuan

For an integer $q\ge 2$, a perfect $q$-hash code $C$ is a block code over $[q]:=\{1,\dots ,q\}$ of length $n$ in which every subset $\{\mathbf{c}_1,\mathbf{c}_2,\dots,\mathbf{c}_q\…