8 problems

MDS Conjecture. The stated upper bound holds for the length $R$ of $C$. Despite significant progress, the MDS Conjecture remains open in general for larger values of $k$ and $q$.

A classical $q$-ary MDS code is an error-correcting code meeting the Singleton bound with equality; let its length be $n$. MDS conjecture. The length is conjectured to satisfy…

A $q$-ary MDS code is a linear code over the field with $q$ elements attaining the Singleton bound; it is nontrivial when it is neither a repetition code, its dual, nor the full ve…

QMDS conjecture. With this exception, the length of every stabilizer QMDS code with $d\geq 3$ satisfies

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

An $\mathbb F_q$-$[N,k,d]$ MDS code is a linear code over $\mathbb F_q$ of length $N$, dimension $k$, and minimum distance $d$. MDS conjecture. Any $\mathbb F_q$-$[N,k,d]$ MDS code…

Let $q$ be a prime power, and let $n$ be the length of a classical $q$-ary MDS code. The classical MDS length bound conjecture. It is conjectured that $n\leq q+2$. The paper contra…

A $q$-ary maximum distance separable (MDS) code is a code attaining the Singleton bound, and a code is nontrivial when its parameters exclude the standard degenerate cases. The cla…