Abstract
In this paper we extend the work of Lisonek and Singh on construction X for quantum error-correcting codes to finite fields of order p 2 where p is prime. Further, we give some new results on the Hermitian dual of repeated root cyclic codes. These results are used to construct new quantum error-correcting codes.
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References
Guenda, K.: Sur l’équivalence des codes. Ph.D. thesis, Faculty of Mathematics, USTHB, Algiers (2010)
Guenda, K., Gulliver, T.A.: Symmetric and asymmetric quantum codes. Int. J. Quantum Inf. 11(5) 1350047 [10 pages] DOI:10.1142/S0219749913500470 (2013)
Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, New York (2003)
Ketkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52(11), 4892–4914 (2006)
Lisonek, P., Singh, V.K.: Quantum codes from nearly self-orthogonal quaternary linear codes. Des. Codes Cryptogr. 73(2), 417–424 (2014)
Rotman, J.J.: Advanced Modern Algebra, 2nd edn. Prentice Hall, Upper Saddle River (2003)
Shor, P.W.: Scheme for reducing decoherence in quantum memory. Phys. Rev. A 52(4), 2493–2493 (1995)
Steane, A.: Multiple particle interference and quantum error correction. Proc. R. Soc. A 452(1954), 2551–2577 (1996)
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Appendix: Code Construction Examples
Appendix: Code Construction Examples
In this appendix, comprehensive tables of codes generated using the results in the paper are presented. Table 1 presents quantum codes obtained using Theorem 4. Many of these codes have parameters better than the best known binary quantum codes. Table 2 presents the parameters of quantum codes obtained from repeated root cyclic codes using Theorem 9. These are codes of length 3p s over fields of size p 2.
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Degwekar, A., Guenda, K., Gulliver, T.A. (2015). Extending Construction X for Quantum Error-Correcting Codes. In: Pinto, R., Rocha Malonek, P., Vettori, P. (eds) Coding Theory and Applications. CIM Series in Mathematical Sciences, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-17296-5_14
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DOI: https://doi.org/10.1007/978-3-319-17296-5_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17295-8
Online ISBN: 978-3-319-17296-5
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