Self-dual Codes With Symplectic Inner Product

In this paper, we firstly give some preliminaries, next present the standard form of a generator matrix for a linear code over ZPm. Future more we introduce an efficient method for constructing self-dual or self-orthogonal over finite rings ZPm with p an odd prime and m a positive integer. We discuss the linear code over Symplectic inner product, which is different from the original inner products—Euclidean inner product. Accoding to the definition of Symplectic inner product, the codes under the Symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a Symplectic self-dual code. In addition, we give a method for constructing a new Symplectic self-dual codes over Fp, which is simpler than others.