Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product

Abstract

In this paper, we consider a family of one-generator quasi-cyclic codes and their applications in quantum codes construction. We give a sufficient condition for self-orthogonality with respect to Hermitian inner product. By virtue of the well-known MacWilliams equations, some binary and ternary stabilizer quantum codes with good parameters are constructed. Furthermore, we present a lower bound on the Hermitian dual distance of these involved codes. As the computational results, some good stabilizer quantum codes over small finite fields are obtained.