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https://hdl.handle.net/2440/3584
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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 1520-6610 |
Statement of Responsibility: | 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 www.wiley.com |
Rights: | Copyright © 2004 John Wiley & Sons, Inc. All Rights Reserved. |
DOI: | 10.1002/jcd.20010 |
Published version: | http://www3.interscience.wiley.com/cgi-bin/abstract/107640520 |
Appears in Collections: | Aurora harvest Pure Mathematics publications |
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