9 problems

Fix an error weight $t$, set $n=n_{\rm min}(t)$, and consider the family of real minimal qubit permutation-invariant quantum error-correcting codes with parameters $(n,t)$. Real mi…

Let a minimal qubit permutation-invariant code have real codeword coefficients, written as $\alpha_i$ and $\beta_i$, with minimal block length $n_{\rm min}$ for error weight $t$. T…

Let a qubit permutation-invariant quantum error-correcting code correct errors of weight at most $t$, and let $n_{\rm min}(t)$ denote the smallest block length among such codes. Th…

Let $t$ be an odd prime number. Consider the nested clique graph with respect to the permutations in beqrefbpermsd, and let $bmathcal Cd$ be the associated $B$-form code. Its lengt…

Let a boolean function determine a code, and let its $bI,H,Nd^n$ spectrum be obtained from the tensor-product transformations indexed by $bI,H,Nd^n$. Let the distance of the code a…

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…