Asymmetric quantum Reed-Solomon and generalized Reed-Solomon codes

Asymmetric quantum Reed-Solomon and generalized Reed-Solomon codes Two new families of asymmetric quantum codes are constructed in this paper. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to classical Reed-Solomon (RS) codes, providing quantum codes with parameters [[N = l(q l −1), K = l(q l −2d + c + 1), d z ≥ d/d x ≥ (d−c)]] q , where q is a prime power and d > c + 1, c ≥ 1, l ≥ 1 are integers. The second family is derived from the CSS construction applied to classical generalized RS codes, generating quantum codes with parameters [[N = mn, K = m(2k−n + c), d z ≥ d/d x ≥ (d−c)]] q , where q is a prime power, 1 < k < n < 2k + c ≤ q m , k = n − d + 1, and n, d > c + 1, c ≥ 1, m ≥ 1 are integers. Although the second proposed construction generalizes the first one, the techniques developed in both constructions are slightly different. These new codes have parameters better than or comparable to the ones available in the literature. Additionally, the proposed codes can be utilized in quantum channels having great asymmetry, that is, quantum channels in which the probability of occurrence of phase-shift errors is large when compared to the probability of occurrence of qudit-flip errors. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Asymmetric quantum Reed-Solomon and generalized Reed-Solomon codes

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Physics, general; Theoretical, Mathematical and Computational Physics; Quantum Physics; Computer Science, general; Mathematics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0269-3
Publisher site
See Article on Publisher Site

Abstract

Two new families of asymmetric quantum codes are constructed in this paper. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to classical Reed-Solomon (RS) codes, providing quantum codes with parameters [[N = l(q l −1), K = l(q l −2d + c + 1), d z ≥ d/d x ≥ (d−c)]] q , where q is a prime power and d > c + 1, c ≥ 1, l ≥ 1 are integers. The second family is derived from the CSS construction applied to classical generalized RS codes, generating quantum codes with parameters [[N = mn, K = m(2k−n + c), d z ≥ d/d x ≥ (d−c)]] q , where q is a prime power, 1 < k < n < 2k + c ≤ q m , k = n − d + 1, and n, d > c + 1, c ≥ 1, m ≥ 1 are integers. Although the second proposed construction generalizes the first one, the techniques developed in both constructions are slightly different. These new codes have parameters better than or comparable to the ones available in the literature. Additionally, the proposed codes can be utilized in quantum channels having great asymmetry, that is, quantum channels in which the probability of occurrence of phase-shift errors is large when compared to the probability of occurrence of qudit-flip errors.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 3, 2011

References

  • On quantum and classical BCH codes
    Aly, S.A.; Klappenecker, A.; Sarvepalli, P.K.
  • Quantum twisted codes
    Bierbrauer, J.; Edel, Y.
  • Concatenated quantum codes constructible in polynomial time: efficient decoding and error correction
    Hamada, M.
  • Constructions of new families of nonbinary CSS codes
    La Guardia, G.G.; Palazzo, R.
  • New quantum MDS codes
    La Guardia, G.G.

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