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arXiv · 1201.4960

A recursive construction of t-wise uniform permutations

Hilary Finucane·Ron Peled·Yariv Yaari
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Abstract

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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Hilary Finucane, Ron Peled, Yariv Yaari. 2012-01-24. A recursive construction of t-wise uniform permutations. https://arxiv.org/abs/1201.4960

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