Self-Dual Codes with Symplectic Inner Product (Communications in Mathematical Research, 2021)
In this paper, we discuss a kind of Hermitian inner product — symplecticinner product, which is different from the original inner product — Euclidean innerproduct. According to the definition of symplectic inner product, the codes underthe symplectic inner product have better properties than those under the generalHermitian inner product. Here we present the necessary and sufficient condition forjudging whether a linear code $C$ over $F_p$ with a generator matrix in the standardform is a symplectic self-dual code. In addition, we give a method for constructing anew symplectic self-dual codes over $F_p$, which is simpler than others.
Keywords: symplectic inner product; symplectic self-dual code; symplectic circulant code.