Construction of linear codes with various Hermitian hull dimensions and related EAQECCs
Ruowen Liu, Shitao Li, Minjia Shi · Advances in Mathematics of Communications · 2024
The hull of a linear code is the intersection of the code and its dual code, which is effective for determining parameters of entanglement-assisted quantum error-correcting codes (EAQECCs). There are few constructions of linear codes with various Hermitian hull dimensions, aside from Hermitian LCD and self-orthogonal codes. The object of this paper is to introduce a building-up construction for constructing linear $ [n+2, k+1] $ codes with $ \ell $ or $ (\ell+1) $-dimensional Hermitian hull from a given linear $ [n, k] $ code with $ \ell $-dimension Hermitian hull of a smaller length. This construction includes the converse of the famous shortening technique as a special case. Using this method, we construct optimal quaternary linear codes of lengths up to 13 with Hermitian hull dimensions 2-5. As an application, we construct many EAQECCs, which improve the parameters of EAQECCs of Grassl's code table.