Constructing quantum error-correcting codes for p^m-state systems from classical error-correcting codes

Abstract

We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of quantum codes with efficient decoding algorithms.

10 pages, LaTeX2e. To appear in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (ISSN 0916-8508), vol. E83-A, no. 10, Oct. 2000. Revision on Dec. 14, 1999: Added a note on a systematic construction of quantum codes with efficient decoding algorithms. Revision on June 26, 2000: Corrected lots of errors, and added a review on the overall error correction process. No original materials were added

References in corpus (2)

• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum Error Correction and Orthogonal Geometry

Cited by in corpus (6)

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• On the distance of stabilizer quantum codes from $J$-affine variety codes
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• Advance sharing of quantum shares for classical secrets
• Stabilizer quantum codes defined by trace-depending polynomials