Quadratic rotation symmetric Boolean functions

04/25/2023

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by   Alexandru Chirvasitu, et al.

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Let (0, a_1, …, a_d-1)_n denote the function f_n(x_0, x_1, …, x_n-1) of degree d in n variables generated by the monomial x_0x_a_1⋯ x_a_d-1 and having the property that f_n is invariant under cyclic permutations of the variables. Such a function f_n is called monomial rotation symmetric (MRS). Much of this paper extends the work on quadratic MRS functions in a 2020 paper of the authors to the case of binomial RS functions, that is sums of two quadratic MRS functions. There are also some results for the sum of any number of quadratic MRS functions.