Quantum Error-correcting Codes Over Finite Abelian Groups

Quantum computing and quantum communication are hot issues,among which strong anti-jamming ability is one of the necessary guarantees for the realization of quantum computing and quantum communication,and the birth of quantum error-correcting code can well solve some interference problems in the communication process.General quantum error-correcting codes are constructed over finite fields,which has some limitations.In this paper,we construct quantum error-correcting codes over finite abelian groups,including additive quantum error-correcting codes and non-additive quantum error-correcting codes.The quantum Hamming bound,the quantum Singleton bound and the most important Mac Williams identity over finite abelian groups are obtained.