6 problems

Let $k$ be an even positive integer and let $n>k$ be an integer. Write $d_2^{E}(n,k)$ for the relevant extremal minimum distance of binary LCD codes, and call a binary LCD code eve…

Let $q$ be a prime power with $q\geq 3$, and let $\mathcal{X}$ be the maximal hyperelliptic curve over $\mathbb{F}_{q^2}$ given by … Let $u_B\in\mathbb{F}_{q^2}[x]$ be an irreducib…

Let $v\geq 0$ and $\mathcal{T}\geq 1$, and consider binary polycyclic codes associated with … Here, an LCD code is a binary linear code whose intersection with its Euclidean dual i…

For positive integers $n$ and $k$, let $d_{LCD}(n,k)$ denote the largest possible minimum distance among binary LCD $[n,k]$ codes. Unit-step conjecture for optimal LCD distances. F…

Let $d_{\mathrm{LCD}}(n,k)$ denote the maximum possible minimum distance $d$ among binary $[n,k,d]$ LCD codes. Galvez et al.'s monotonicity conjecture. For any $k$, one has … This…

Let $q$ be odd and $m \geq 2$. For an integer $t$ with $1 \leq t \leq \bar m$, let $\delta=(q^t-1)/2$ and let ${\mathcal{C}}_{(q,n,2\delta,\frac{n}{2}-\delta+1)}$ be the code from…