CryptoDB
Geometric constructions of optimal linear perfect hash families
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| Abstract: | A linear $(q^d,q,t)$-perfect hash family of size $s$ in a vector space $V$ of order $q^d$ over a field $F$ of order $q$ consists of a sequence $\phi_1,\ldots,\phi_s$ of linear functions from $V$ to $F$ with the following property: for all $t$ subsets $X\subseteq V$ there exists $i\in\{1,\ldots,s\}$ such that $\phi_i$ is injective when restricted to $F$. A linear $(q^d,q,t)$-perfect hash family of minimal size $d(t-1)$ is said to be optimal. In this paper we use projective geometry techniques to completely determine the values of $q$ for which optimal linear $(q^3,q,3)$-perfect hash families exist and give constructions in these cases. We also give constructions of optimal linear $(q^2,q,5)$-perfect hash families. |
BibTeX
@misc{eprint-2006-21496,
title={Geometric constructions of optimal linear perfect hash families},
booktitle={IACR Eprint archive},
keywords={applications / perfect hash families},
url={http://eprint.iacr.org/2006/002},
note={ sue.barwick@adelaide.edu.au 13151 received 3 Jan 2006},
author={S.G. Barwick and W.-A. Jackson.},
year=2006
}