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arXiv · 1303.3527

Classification of Boolean Functions where Affine Functions are Uniformly Distributed

Ranjeet Kumar Rout·Pabitra Pal Choudhury·Sudhakar Sahoo
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Abstract

Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where only one affine Boolean function belongs to each class. Two different methods are proposed to achieve this classification. The first method is a recursive procedure that uses the Cartesian product of sets starting from the set of 1-variable Boolean function and in the second method classification is achieved through a set of invariant bit positions with respect to an affine function belonging to that class. The invariant bit positions also provide information concerning the size and symmetry properties of the classes/sub-classes, such that the members of classes/sub-classes satisfy certain similar properties.

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Ranjeet Kumar Rout, Pabitra Pal Choudhury, Sudhakar Sahoo. 2013-03-12. Classification of Boolean Functions where Affine Functions are Uniformly Distributed. https://arxiv.org/abs/1303.3527

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