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**2003/017**

**Title:**

Perfect Hash Families with Few Functions

**Authors:**
Simon R. Blackburn

**Abstract:**

An {\em (s;n,q,t)-perfect hash family} is a set of functions

\phi_1,\phi_2,\ldots ,\phi_s from a set V of cardinality n to a

set F of cardinality q with the property that every t-subset of

V is injectively mapped into F by at least one of the functions

\phi_i.

The paper shows that the maximum value n_{s,t}(q) that n can take

for fixed s and t has a leading term that is linear in q if and only if

t>s. Moreover, for any s and t such that t>s, the paper shows how to

calculate the coefficient of this linear leading term; this

coefficient is explicitly calculated in some cases. As part of this

process, new classes of good perfect hash families are constructed.

**ePrint:**
https://eprint.iacr.org/2003/017

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