6 problems

Song–Cai–Yue conjecture. An achievable upper bound on the rate $k/n$ is

Locality conjecture. In the cases not covered by the preceding proved locality results, the asserted localities hold. This would complete the locality description for…

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…

Zero-count conjecture. Any function $f\in V$ will have fewer than

Let $q$ be the alphabet size, and let an optimal locally recoverable code have minimum distance $d$ and locality $r$. Length conjecture for optimal locally recoverable codes. Every…

Let ${\sf Cap}_{\rm BSC}(p,\rho,r)$ denote the capacity of locally recoverable codes over the binary symmetric channel with crossover probability $p$ and locality parameter $r$, an…