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

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

**Example resources include:**
implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .