T. Cusick

activity

20062025

most citedBalanced Symmetric Functions over

GF (p)

2 citations · 2 across the 3 of their papers we have counts for

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cs.IT2025

Recursions for quadratic rotation symmetric functions weights

Thomas W. Cusick

A Boolean function in $n$ variables is rotation symmetric (RS) if it is invariant under powers of $ρ (x_{1}, \dots, x_{n}) = (x_{2}, \dots, x_{n}, x_{1})$ . An RS function is called monomial…

cs.IT2019

Symbolic dynamics and rotation symmetric Boolean functions

Alexandru Chirvasitu, Thomas Cusick

We identify the weights $w t (f_{n})$ of a family ${f_{n}}$ of rotation symmetric Boolean functions with the cardinalities of the sets of $n$ -periodic points of a finite-type shift, re…

cs.IT2019

Affine equivalence for quadratic rotation symmetric Boolean functions

Alexandru Chirvasitu, Thomas W. Cusick

Let $f_{n} (x_{0}, x_{1}, \dots, x_{n - 1})$ denote the algebraic normal form (polynomial form) of a rotation symmetric (RS) Boolean function of degree $d$ in $n \geq d$ variables and let…

cs.IT2017

Rotation Symmetric Bent Boolean Functions for n = 2p

T. W. Cusick, E. M. Sanger

It has been conjectured that there are no homogeneous rotation symmetric bent Boolean functions of degree greater than two. In this paper we begin by proving that sums of short-cyc…