6 problems

Khesin–Lu–Shor distance conjecture. For $m\geq 7$, the distance is $d(m)=m$. This would determine the distance of the Hamming-code-derived family in the stated parameter range; the…

Let $[n,k,d]$ be a CSS code, and let a stabilizer check of weight $m\geq5$ be replaced by two checks through the bridged-star vertex-reduction construction, producing a new CSS cod…

Let a CSS code be represented by a chain complex, and suppose that the $X$- and $Z$-stabilizer sets have even sizes, so that stabilizers can be randomly paired and spliced independ…

A CSS code is obtained from a Coxeter group and its Bruhat order, with the code parameters determined by the associated Bruhat-poset construction. Family conjecture. Almost all suc…

Minimality conjecture. CSS codes constructed from extremal type-II self-dual codes are the smallest stabilizer codes with transversal single-qubit Clifford group for their respecti…

Consider the subspace CSS code obtained by applying the paper's stabilizer-to-CSS mapping to the double semion code, with two physical qudits per edge and eight stabilizer generato…