T. Cusick

activity

20002026

most citedAffine equivalence of cubic homogeneous rotation symmetric Boolean functions

41 citations · 44 across the 11 of their papers we have counts for

collaborators

14 papers

math.CO2026

Equality Cases in the Tu-Deng Conjecture Bound

Thomas W. Cusick

The Tu-Deng Conjecture, made in 2011, asserts that for $k \geq 2$ and $1 \leq t < 2^{k} - 1$ , the set \[ S_{t,k}=\left\{(a,b)\in\{0,1,\ldots,2^k-2\}^2: a+b\equiv t\pmod{2^k-1},\quad \wt(a)+…

math.DS2026

The Quadratic Easy Coefficients Conjecture via Finite-Type Shifts and Zeta Functions

Thomas W. Cusick

We prove the Quadratic Easy Coefficients Conjecture stated as Conjecture 1 in T. W. Cusick, \emph{Recursions for quadratic rotation symmetric functions weights}, Discrete Applied M…

math.CO2026

Proof of the TuDeng Conjecture

Thomas W. Cusick

We give a complete proof of the 2011 Tu--Deng conjecture. We begin from its original modular pair-count formulation, prove an equivalent cyclic Hamming weight-drop formulation, and…

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…

math.CO2023

Quadratic rotation symmetric Boolean functions

Alexandru Chirvasitu, Thomas W. Cusick

Let $(0, a_{1}, \dots, a_{d - 1})_{n}$ denote the function $f_{n} (x_{0}, x_{1}, \dots, x_{n - 1})$ of degree $d$ in $n$ variables generated by the monomial $x_{0} x_{a_{1}} \dots x_{a_{d - 1}}$ and…

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…