Explicit constructions for perfect hash families

Let k, v, t be integers such that k ≥ v ≥ t ≥ 2. A perfect hash family PHF(N ; k, v, t) can be defined as an N × k array with entries from a set of v symbols such that every N× t subarray contains at least one row having distinct symbols. Perfect hash families have been studied by over 20 years and they find a wide range of applications in computer sciences and in cryptography. In this paper we focus on explicit constructions for perfect hash families using combinatorial methods. We present many recursive constructions which result in a large number of improved parameters for perfect hash families. The paper also includes extensive tables for parameters with t = 3, 4, 5, 6 of newly constructed perfect hash families.