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Constructions of involutions with optimal minimum degree

Constructions of involutions with optimal minimum degree

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The minimum degree (resp. algebraic degree) of a Boolean permutation is the minimum (resp. maximum) algebraic degree of all the non-zero linear combinations of its coordinate functions. In this study, the authors concentrate on the design of Boolean permutations with optimal minimum degree. First, they present a novel method for optimising the minimum degrees of known Boolean permutations. Second, they show that the Boolean permutations, which are obtained by optimising Boolean permutations without optimal algebraic degree, have optimal minimum degree. At last, it is shown that their method generates an infinite class of involutions with optimal minimum degree.

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