5 problems

Maximum-length conjecture. Apart from some exceptions, the maximum length of an EAQMDS code over the relevant field is

A quantum MDS code is called non-trivial when it is not one of the degenerate parameter families excluded in the usual quantum MDS length question. Quantum MDS length-bound conject…

For $q=2^m$, consider quantum MDS codes over systems of dimension $q$, with parameters written as $[[n,n-6,4]]_{2^m}$. Binary-extension QMDS existence conjecture. If $q=2^m$ and…

Let $q$ be a prime power and let $C^*=[q^2+1,q^2+1-d,d]_{q^2}$ be an $F_{q^2}$-linear (consta)cyclic MDS code. Let $P(C)$ denote its corresponding puncture code. Puncture-code dist…

A quantum MDS (QMDS) code over systems of dimension $q$ has a length $n$ and minimum distance $d$; shortening a QMDS code of length $q^2+1$ produces QMDS codes at shorter admissibl…