[Resource Topic] 2006/002: Geometric constructions of optimal linear perfect hash families

Welcome to the resource topic for 2006/002

Title:
Geometric constructions of optimal linear perfect hash families

Authors: S. G. Barwick, W. -A. Jackson.

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.

ePrint: https://eprint.iacr.org/2006/002

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