4 problems

Let ${\mathfrak C}$ be a minor-closed family of binary linear codes. A code is an excluded minor of ${\mathfrak C}$ if it does not belong to ${\mathfrak C}$ while every proper mino…

Let $d(n,5)$ denote the maximum minimum distance of a binary linear $[n,5]$ code, and let $d_{\mathrm{so}}(n,5)$ denote the maximum minimum distance of a binary self-orthogonal…

Let $C$ be a binary linear $[k+3,k]_2$ code, and let $M_2(k+3,k)$ denote the maximum possible number of minimal codewords among such codes. For $k\geq 4$, write … where the entries…

Let $A$ be the adjacency matrix of a graph $\Gamma$ on $n$ vertices with vertex set $V$. Let $C$ be the binary linear code generated by $[I_n|A]$, and let $d(C)$ denote its minimum…