Ternary Quantum Codes Constructed from a Class of Quasi-Twisted Codes

Abstract

In this paper, we propose a class of 1-generator quasi-twisted codes with special structures and investigate their application to construct ternary quantum codes. We discuss the algebraic structure of these 1-generator quasi-twisted codes and their dual codes. Moreover, sufficient conditions for these quasi-twisted codes to satisfy Hermitian self-orthogonality are given. Then, some ternary quantum codes exceeding the Gilbert-Varshamov bound are derived from such Hermitian self-orthogonal 1-generator quasi-twisted codes. In particular, sixteen quantum codes are new or have better parameters than those in the literatures, eight of which are obtained by the progapation rules.