Quantum Codes Derived from Two Construction Methods

Abstract

There are mainly two efficient constructing methods for quantum codes, the construction named after Calderbank, Shor and Stean, and the hermitian code construction. We compare two methods in quantum cyclic codes and quantum duadic codes separately, and show that the hermitian code construction is better in terms of existence conditions of codes and the code parameters.Keywords-nonbinary quantum code; hermitian code construction; quantum cyclic code; quantum duadic code.