5 problems

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

For each $r\geq 2$, let $A_{r,r-1}$ be the explicitly constructed $(r,r-1)$-erasure correcting set, and let $F(r,r-1)$ be the minimum cardinality of any such set. Smallest-set conj…

Let $F(r,m)$ denote the smallest cardinality of an $(r,m)$-erasure correcting set, and let $A_{r,m}$ be the construction described in the paper. Optimality conjecture. If $r\geq 2$…

Regularity characterization conjecture. An erasure pattern $E$ is correctable for $T_{m\times n}(a,b,0)$ if and only if it is regular.

Distance-property conjecture. The results obtained for the ensemble considered in this work may give, as a first approximation, hints on the distance properties of Raptor codes emp…