A recursive construction of t-wise uniform permutations

Details A recursive construction of t-wise uniform permutations A recursive construction of t-wise uniform permutations

2012-01-24

arxiv.org/abs/1201.4960v1

Mathematics

Combinatorics

Scientific paper

We present a recursive construction of a (2t + 1)-wise uniform set of permutations on 2n objects using a (2t + 1) - (2n, n, \cdot) combinatorial design, a t-wise uniform set of permutations on n objects and a (2t+1)-wise uniform set of permutations on n objects. Using the complete design in this procedure gives a t-wise uniform set of permutations on n objects whose size is at most t^2n, the first non-trivial construction of an infinite family of t-wise uniform sets for t \geq 4. If a non-trivial design with suitable parameters is found, it will imply a corresponding improvement in the construction.

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