NONBINARY QUANTUM CODES DERIVED FROM GROUP CHARACTER CODES

Most of quantum codes have been constructed by using classical linear codes over finite field. However, little is known about the construction of quantum codes via group character codes. In this work, we present the constructions of nonbinary quantum and asymmetric quantum codes based on group character codes, and give explicit parameters for infinite families of nonbinary quantum codes and asymmetric quantum codes. Furthermore, we present families of optimal quantum codes which derived from group character codes.

[1]  Zongben Xu,et al.  On [[n,n-4,3]]q Quantum MDS Codes for odd prime power q , 2009, ArXiv.

[2]  Pradeep Kiran Sarvepalli,et al.  On Quantum and Classical BCH Codes , 2006, IEEE Transactions on Information Theory.

[3]  Reginaldo Palazzo Júnior,et al.  Constructions of new families of nonbinary CSS codes , 2010, Discret. Math..

[4]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[5]  San Ling,et al.  A family of group character codes , 2004, Eur. J. Comb..

[6]  Santosh Kumar,et al.  Nonbinary Stabilizer Codes Over Finite Fields , 2005, IEEE Transactions on Information Theory.

[7]  N. J. A. Sloane,et al.  Quantum Error Correction Via Codes Over GF(4) , 1998, IEEE Trans. Inf. Theory.

[8]  Chaoping Xing,et al.  Asymmetric Quantum Codes: Characterization and Constructions , 2010, IEEE Transactions on Information Theory.

[9]  M. Mézard,et al.  Asymmetric quantum error-correcting codes , 2006, quant-ph/0606107.

[10]  Chaoping Xing,et al.  Asymptotic bounds on quantum codes from algebraic geometry codes , 2006, IEEE Transactions on Information Theory.

[11]  Xueliang Li,et al.  Binary Construction of Quantum Codes of Minimum Distance Three and Four , 2004, IEEE Trans. Inf. Theory.