2 problems

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Shi et al.'s conjecture on the maximum number of nonzero Hamming weights
Shi et al.'s conjecture. The bound is tight for all values of $q$ and $k$ .
Conjecturesolvedcoding-theory hamming-metric weight-spectraarXiv posted 2 days ago
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Wang–Feng–Kovács conjecture on maximum intersections of permutation Hamming balls
Wang–Feng–Kovács conjecture. For any $r\ge 5$ and $n\ge r$ , one has
Conjectureopencoding-theory hamming-metric permutation-groupsarXiv posted 2 days ago

Shi et al.'s conjecture on the maximum number of nonzero Hamming weights