Asymmetric quantum codes: new codes from old

  • Authors:

  • Giuliano G. La Guardia

  • Affiliations:

  • Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, Brazil 84030-900

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2013

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Abstract

In this paper we extend to asymmetric quantum error-correcting codes the construction methods, namely: puncturing, extending, expanding, direct sum and the $$({ \mathbf u}| \mathbf{u}+{ \mathbf v})$$ construction. By applying these methods, several families of asymmetric quantum codes can be constructed. Consequently, as an example of application of quantum code expansion developed here, new families of asymmetric quantum codes derived from generalized Reed-Muller codes, quadratic residue, Bose-Chaudhuri-Hocquenghem, character codes and affine-invariant codes are constructed.