Circulant matrices and affine equivalence of monomial rotation symmetric Boolean functions
Discrete Mathematics(2015)
摘要
The goal of this paper is two-fold. We first focus on the problem of deciding whether two monomial rotation symmetric (MRS) Boolean functions are affine equivalent via a permutation. Using a correspondence between such functions and circulant matrices, we give a simple necessary and sufficient condition. We connect this problem with the well known Ádám's conjecture from graph theory. As applications, we reprove easily several main results of Cusick et¿al. on the number of equivalence classes under permutations for MRS in prime power dimensions, as well as give a count for the number of classes in p q number of variables, where p , q are prime numbers with¿ p
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关键词
Boolean functions,Circulant matrices,Affine equivalence,Permutations
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