Symplectic self-orthogonal quasi-cyclic codes

Abstract

In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of $1$-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct numerous new binary symplectic self-orthogonal QC codes with excellent parameters, leading to $117$ record-breaking quantum error-correction codes.

This paper was published in IEEE TIT. In this version, we have corrected some minor errors, among which the most significant change is that the constraint $\gcd ({\bar{f}}_0(x),g(x))=1$ in Theorem 5 has been corrected to $\gcd (f_0(x),g(x))=1$