7 problems

Construction 2 weight-spectrum conjecture. The set $S$ contains all weights in the two families

KasamiCarlet weight-spectrum conjecture. For any positive integer $c$ and $m\ge 2c$, the weight spectrum of $RM(m-c,m)$ is of the form

Shi et al.'s conjecture. The largest number of non-zero weights of $\mathcal{C}$ is bounded above by

The weight-distribution conjecture. The polynomial $f(x)$ is two-to-one over ${\mathbb F}_{2^n}$, the code $\mathcal{C}_{D(f)}$ has parameters

Maximum distinct-weight conjecture. The maximum number of distinct nonzero weights that a $k$-dimensional $q$-ary code can have is

Let $\mathrm{C}$ be the set of all linear codes with non-trivial parameters $q\geq 2$ and $n>k>0$. For $C\in\mathrm{C}$, let $h(C)$ be the smallest number such that fixing any…

Let $Q\subset \mathbb F_2^n$ be an $\mathbb F_2$-linear code, and let $\mu_{Q+u}$ be the uniform probability distribution on the coset $Q+u$. Write $\overline{\mu_{Q+u}}$ for its w…