Let V be a set of order n and let F be a set of order q. A set S [,: V Ä F ] of functions from V to F is an (n, q, t)-perfect hash family if for all X V with |X | =t, there exists , # S which is injective when restricted to X. Perfect hash families arise in compiler design, in circuit complexity theory and in cryptography. Let S be an (n, q, t)-perfect hash family. The paper provides lower bounds on |S|, which better previously known lower bounds for many parameter sets. The paper exhibits new classes of perfect hash families which show that these lower bounds are realistic.
Academic Press
A perfect binary array is an r-dimensional array with elements k 1 such that all out-of-phase periodic autocorrelation coefficients are zero. Such an array is equivalent to a Menon difference set in an abelian group. We give recursive constructions for four infinite families of two-dimensional perfect binary arrays, using only elementary methods. Brief outlines of the proofs were previously given by three of the authors. Although perfect binary arrays of the same sizes as two of the families were constructed earlier by Davis, the sizes of the other two families are new.
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