3 problems

Shi et al.'s conjecture. The bound is tight for all values of $q$ and $k$.

Let $RM(r,m)$ denote the Reed–Muller code of order $r$ in $m$ variables, and let its weight spectrum be the set of Hamming weights of its codewords. For a set $S$ of weights, write…

Let $RM(m-c,m)$ denote the binary Reed–Muller code of order $m-c$ in $m$ variables, and let its weight spectrum be the set of Hamming weights of its codewords. For a set of weights…