The paper proves that for every k≥2 and each nonzero t below 2^k−1, the number of binary pairs with weight sum below k and sum congruent to t modulo 2^k−1 is at most 2^{k−1}.
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Proof of the TuDeng Conjecture
The paper proves that for every k≥2 and each nonzero t below 2^k−1, the number of binary pairs with weight sum below k and sum congruent to t modulo 2^k−1 is at most 2^{k−1}.