On symplectic hulls of linear codes and related applications

This paper investigates symplectic hulls of linear codes. We use a different view to obtain more structural properties of generator matrices with respect to the symplectic inner product. As an outgrowth, generalized formulas for calculating dimensions of symplectic hulls are derived, which extend some known results in the literature. We then study the symplectic hull-variation problem and prove that a monomially equivalent linear code with a smaller dimensional symplectic hull can always be explicitly derived from a given q-ary symplectic self-dual code with a standard generator matrix for \(q\ge 3\) $q\ge 3$ . As an application, we present an improved propagation rule for constructing entanglement-assisted quantum error-correcting codes (EAQECCs) and obtain some new and record-breaking binary EAQECCs.