Algorithms for computing the permutation resemblance of functions over finite groups

02/08/2023

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by   Li-An Chen, et al.

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Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing feasible solutions to this integer program, and use it to prove an upper bound for permutation resemblance for some special functions. Additionally, we present a generalization of the linear integer program that takes a function on a finite group and determines a permutation with the lowest differential uniformity among those most resembling it.