8 problems

Common-zero conjecture. Any such element has at least $4$ zeros in common with each of the elements $x_1-\alpha$ and $x_2-\beta$. This anticipated common-zero property is used to c…

Zero-bound conjecture. No element of $V$ has more than $48-4=44$ zeros in $\mathcal{B}$. This bound is intended to provide the distance estimate for the constructed locally repaira…

Maximum-distance conjecture. It is not possible to have minimum distance $d=10$ in this case, and the largest minimum distance achievable is

Non-equivalence conjecture. Not every LRCC attaining this bound for some $j\in\mathbb{N}$ is a partial $j$-MDS convolutional code.

Conjecture for $\alpha_5$ and $\alpha_6$. The parameter tuples are

Rate upper-bound conjecture. An achievable upper bound on the rate of an $(n,k,r,t)$-SLRC is

The paper constructs matroids in Section 4; write $n$ for their ground-set size and say that a matroid is representable over a field if it arises from a matrix over that field. Rep…

Consider codes of positive rate for the binary erasure channel, without assuming that the encoding is linear. Logarithmic update-complexity conjecture. Every such code must have up…