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Optimal linear perfect hash families with small parameters

✍ Scribed by S. G. Barwick; Wen-Ai Jackson; Catherine T. Quinn

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 146 KB
Volume: 12
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20010

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✦ Synopsis

Abstract

A linear (q^d^, q, t)‐perfect hash family of size s consists of a vector space V of order q^d^ over a field F of order q and a sequence ϕ~1~,…,ϕ~s~ of linear functions from V to F with the following property: for all t subsets X ⊆ V, there exists i ∈ {1,·,s} such that ϕ~i~ is injective when restricted to F. A linear (q^d^, q, t)‐perfect hash family of minimal size d( – 1) is said to be optimal. In this paper, we prove that optimal linear (q^2^, 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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