MDS codes with Euclidean and Hermitian hulls of flexible dimensions and their applications to EAQECCs

The hull of a linear code is the intersection itself with its dual respect to certain inner product. Both Euclidean and Hermitian hulls are theorical practical significance. In this paper, we construct several new classes maximum distance separable (MDS) codes via (extended) generalized Reed-Solomon (GRS) determine their or hulls. As consequence, four MDS flexible dimensions six constructed. applications, for former, further families entanglement-assisted quantum error-correcting (EAQECCs) EAQECCs length $$n>q+1$$ . Meanwhile, many parameters our greater than $$\lceil \frac{q}{2} \rceil $$ q; latter, show some examples on self-orthogonal one-dimensional codes. addition, two general methods constructing extended GRS $$(k-1)$$ -dimensional also provided.