A Complete Proof for Tu-Deng Conjecture

Renzhang Liu, Hengyi Luo, Tianyuan Xie

Let $N=2^k-1$ and let $\mathrm{wt}(n)$ denote the binary Hamming weight. The Tu-Deng conjecture asserts that, for every $1\le t\le N-1$, at most $2^{k-1}$ pairs $(a,b)\in\{0,…