Abstract
AbstractA linear (qd, q, t)‐perfect hash family of size s consists of a vector space V of order qd over a field F of order q and a sequence ϕ1,…,ϕs of linear functions from V to F with the following property: for all t subsets X ⊆ V, there exists i ∈ {1,·,s} such that ϕi is injective when restricted to F. A linear (qd, q, t)‐perfect hash family of minimal size d( – 1) is said to be optimal. In this paper, we prove that optimal linear (q2, q, 4)‐perfect hash families exist only for q = 11 and for all prime powers q > 13 and we give constructions for these values of q. © 2004 Wiley Periodicals, Inc. J Comb Designs 12: 311–324, 2004
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