Inhomogeneous quantum codes (II): non-additive case

Abstract

The quantum codes have been generalized to inhomogeneous case and the stabilizer construction has been established to get additive inhomogeneous quantum codes in [Sci. China Math., 2010, 53: 2501–2510]. In this paper, we generalize the known constructions to construct non-additive inhomogeneous quantum codes and get examples of good d-ary quantum codes.

Keywords

Quantum code / inhomogeneous code / mixed code / finite abelian group / character / quadratic generalized boolean function

References

[1] Calderbank A. R., Rains E. M., PShor P. W., Sloane N. J. A. Quantum error correction via codes over GF(4). IEEE Trans Inf Theory, 1998, 44: 1369-1387

[2] Feng K., Ling S., Xing C. Asymptotic bounds on quantum codes from algebraic geometry codes. IEEE Trans Inf Theory, 2006, 52: 986-991

[3] Feng K., Xing C. A new construction of quantum error-correcting codes. Trans Amer Math Soc, 2007, 360: 2007-2019

[4] Gottesman D. Fault-tolerant quantum computation with high-dimensional systems. LNCS, 1999, 1509: 302-313

[5] Ketkar A., Klappenecker A., Kumar S., Sarvepalli P. K. Nobinary stabilizer codes over finite field. IEEE Trans Inf Theory, 2006, 52: 4892-4914

[6] Wang W., Feng R., Feng K. Inhomogenous quantum codes (I): additive case. Sci China Math, 2010, 53: 2501-2510