6 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…

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…