Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs
share
In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, which we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It turns out that the dimensions of Euclidean hulls or Hermitian hulls of the codes in our constructions can take all or almost all possible values. As a consequence, we can apply our results to entanglement-assisted quantum error-correcting codes (EAQECCs) and obtain several families of MDS EAQECCs with flexible parameters. The required number of maximally entangled states of these MDS EAQECCs can take all or almost all possible values. In particular, all possible parameters for the q-ary MDS EAQECCs of length n≤ q are completely determined and several new classes of q-ary MDS EAQECCs of length n>q are also obtained.
READ FULL TEXT