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Type: Journal article
Title: Geometric constructions of optimal linear perfect hash families
Author: Barwick, S.
Jackson, W.
Citation: Finite Fields and Their Applications, 2008; 14(1):1-13
Publisher: Academic Press Inc
Issue Date: 2008
ISSN: 1071-5797
Statement of
S.G. Barwick, and Wen-Ai Jackson
Abstract: A linear (qd,q,t)-perfect hash family of size s in a vector space V of order qd over a field F of order q consists of a sequence 1,…,s of linear functions from V to F with the following property: for all t subsets XV there exists i{1,…,s} such that i is injective when restricted to F. A linear (qd,q,t)-perfect hash family of minimal size d(t−1) is said to be optimal. In this paper we use projective geometry techniques to completely determine the values of q for which optimal linear (q3,q,3)-perfect hash families exist and give constructions in these cases. We also give constructions of optimal linear (q2,q,5)-perfect hash families.
Keywords: Projective planes; Linear perfect hash families
Rights: © 2007 Elsevier Inc. All rights reserved.
RMID: 0020074994
DOI: 10.1016/j.ffa.2007.09.003
Appears in Collections:Mathematical Sciences publications

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