Optimal linear perfect hash families with small parameters | Zendy

Barwick S. G. | Zendy; Jackson WenAi | Zendy; Quinn Catherine T. | Zendy

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Optimal linear perfect hash families with small parameters

Author(s) -

Barwick S. G.,

Jackson WenAi,

Quinn Catherine T.

Publication year - 2004

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.20010

Subject(s) - mathematics , combinatorics , perfect hash function , hash function , order (exchange) , discrete mathematics , injective function , vector space , linear space , perfect power , algorithm , pure mathematics , cryptography , cryptographic hash function , computer security , finance , computer science , economics

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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