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Type: Journal article
Title: Optimal linear perfect hash families with small parameters
Author: Barwick, S.
Jackson, W.
Quinn, C.
Citation: Journal of Graph Theory, 2004; 12(5):311-324
Publisher: John Wiley & Sons Inc
Issue Date: 2004
ISSN: 1063-8539
Statement of
S. G. Barwick, Wen-Ai Jackson and Catherine T. Quinn
Abstract: A 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(t - 1) is said to be optimal. In this paper, we prove that optimal linear (qd, q, t)-perfect hash families exist only for q = 11 and for all prime powers q > 13 and we give constructions for these values of q.
Keywords: perfect hash families
finite projective geometry
Description: The definitive version may be found at
Rights: Copyright © 2004 John Wiley & Sons, Inc. All Rights Reserved.
DOI: 10.1002/jcd.20010
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Appears in Collections:Aurora harvest
Pure Mathematics publications

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