Quadratic rotation symmetric Boolean functions

Let (0, a1, ... , ad-1)n denote the function fn(x0, x1, ... , xn-1) of degree d in n variables generated by the monomial x0xa1 center dot center dot center dot xad-1 and having the property that fn is invariant under cyclic permutations of the variables. Such a function fn 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.(c) 2023 Elsevier B.V. All rights reserved.