Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 3: 573 - 586

DOI: https://doi.org/10.1007/s11464-012-0209-2

RESEARCH ARTICLE

Inhomogeneous quantum codes (II): non-additive case

  • Weiyang WANG , 1 ,
  • Keqin FENG 2
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  • 1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received date: 06 Jan 2011

Accepted date: 01 Apr 2012

Published date: 01 Jun 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Quantum code; inhomogeneous code; mixed code; finite abelian group; character; quadratic generalized boolean function

Cite this article

Weiyang WANG , Keqin FENG . Inhomogeneous quantum codes (II): non-additive case[J]. Frontiers of Mathematics in China, 2012 , 7(3) : 573 -586 . DOI: 10.1007/s11464-012-0209-2

References

Publishing order | Descend order by publishing year | Descend order by cited within
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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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