6 problems

A Boolean function in an even number of variables is homogeneous if all monomials in its algebraic normal form have the same degree; it is rotation symmetric if it is invariant und…

Let $f^n$ be the cubic rotation symmetric Boolean function in $n$ variables generated by the monomial $x_0x_1x_2$. Its weight $wt(f^n)$ is the number of inputs in $\mathbb{F}_2^n$…

Quadratic Easy Coefficients Conjecture. For $n=1,2,\ldots$, the Hamming weight of the associated function $f_n$ satisfies

Let $I$ be an index set, let $Q_{I,n}$ be the associated rotation-symmetric quadratic Boolean function, and set … Let $w_1,w_2,\ldots$ be the sequence obtained by extending the rec…

Let $l\geq 4$ be an integer, and let $f$ be the rotation symmetric Boolean function generated by the monomial $x_0x_ex_{2e}\cdots x_{le}$, with the parameter $e$ as in the paper's…

Let $B_n$ denote the set of cubic homogeneous rotation symmetric Boolean functions in $n$ variables. Two such functions are affine equivalent if one is obtained from the other by a…