On the Construction of Hermitian Self-Orthogonal Codes Over \(F_9\) and Their Application

We construct a lot of optimal or near-optimal \([n,k,d]_9\) ${[n,k,d]}_9$ Hermitian self-orthogonal codes for \(k\le 3\) $k\le 3$ using norm codes and matrix combinatorial construction method. As an application, we construct nine families of entanglement-assisted quantum error-correcting codes. Some of these codes can achieve q-ary linear EA-Griesmer bound with better parameters than those in the literature.