The Improvement of the Bound on Hash Family

Abstract

In this paper, we study the bound on three kinds of hash family using the Singleton bound. To $\epsilon -U(N;n,m)$ hash family, in the caes of $n>m^2>1$ and $1\ge \epsilon \ge {\epsilon }_1(n,m)$, we get that the new bound is better. To $\epsilon -△U(N;n,m)$ hash family, in the case of $n>m>1$ and $1\ge \epsilon \ge {\epsilon }_3(n,m)$, the new bound is better. To $\epsilon -SU(N;n,m)$ hash family, in the case of $n>2^m>2$ and $1\ge \epsilon \ge {\epsilon }_4(n,m)$, we get that the new bound is better.