T. Cusick

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20002026

most citedAffine equivalence of cubic homogeneous rotation symmetric Boolean functions

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

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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.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…