Optimal linear perfect hash families with small parameters
Date
2004
Authors
Barwick, S.
Jackson, W.
Quinn, C.
Editors
Advisors
Journal Title
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Journal article
Citation
Journal of Combinatorial Designs, 2004; 12(5):311-324
Statement of Responsibility
S. G. Barwick, Wen-Ai Jackson and Catherine T. Quinn
Conference Name
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.
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Dissertation Note
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The definitive version may be found at www.wiley.com
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Copyright © 2004 John Wiley & Sons, Inc. All Rights Reserved.