7 problems

Let $m$ and $t$ be integers, and let $C$ be obtained by adding an overall parity check to the primitive BCH code of length $2^m-1$ and designed distance $2t-1$. Thus $C$ has length…

Ding et al.'s conjecture. The minimum distance is always equal to the Bose distance:

Geng et al.'s AMDS conjecture. The code $\mathcal{C}^\perp_{(q,q+1,3,4)}$ is an AMDS code with parameters $[q+1,4,q-3]$.

Let $q=p^s$, where $p$ is an odd prime and $s\ge 2$, and set $h=\frac{p-1}{2}$. Let $\mathcal{C}_{(q,q+1,3,h)}$ denote the BCH code in question. BCH-code conjecture. The code…

Let $q$ be a power of $2$ and let $n=q^m+1$, with the quantities $\delta_2$ and $\delta_3$ defined as in the preceding cases for even $m$. Second and third largest coset leader con…

Let $q$ be an odd prime power and let $n=q^m+1$, with the quantities $\delta_3$ and $\delta_4$ defined as in the preceding cases for even $m$. Third and fourth largest coset leader…

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…