Characterization and mass formulas of symplectic self-orthogonal and LCD codes and their application

The object of this paper is to study two very important classes of codes in coding theory, namely self-orthogonal (SO) and linear complementary dual (LCD) codes under the symplectic inner product, involving characterization, constructions, and their application. Using such a characterization, we determine the mass formulas of symplectic SO and LCD codes by considering the action of the symplectic group, and further obtain some asymptotic results. Finally, under the Hamming distance, we obtain some symplectic SO (resp. LCD) codes with improved parameters directly compared with Euclidean SO (resp. LCD) codes. Under the symplectic distance, we obtain some additive SO (resp. additive complementary dual) codes with improved parameters directly compared with Hermitian SO (resp. LCD) codes. Further, we also construct many good additive codes outperform the best-known linear codes in Grassl's code table. As an application, we construct a number of record-breaking (entanglement-assisted) quantum error-correcting codes, which improve Grassl's code table.