Welcome to the resource topic for 2005/465
Title:
A sequence approach to constructing 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
set \phi_1,\ldots,\phi_s of linear functionals 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 {\em optimal}. In this paper we
extend the theory for linear perfect hash families based on sequences
developed by Blackburn and Wild. We develop techniques which we use to
construct new optimal linear (q^2,q,5)-perfect hash families and
(q^4,q,3)-perfect hash families. The sequence approach also
explains a relationship between linear (q^3,q,3)-perfect hash
families and linear (q^2,q,4)-perfect hash families.
ePrint: https://eprint.iacr.org/2005/465
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