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The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes

Yıl 2014, Cilt: 1 Sayı: 1, 13 - 17, 01.03.2014
https://doi.org/10.13069/jacodesmath.25090

Öz

The existence of a quantum [[28, 12, 6]] code was one of the few cases for codes of length n ≤ 30 thatwas left open in the seminal paper by Calderbank, Rains, Shor, and Sloane [2]. The main result ofthis paper is the construction of the first optimal linear quaternary [28, 20, 6] code which contains itsHermitian dual code and yields the first optimal quantum [[28, 12, 6]] code

Kaynakça

  • W. Bosma, J. Cannon, J, Handbook of Magma Functions, Department of Mathematics, University of Sydney, 1994.
  • A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, Quantum error correction via codes over GF (4), IEEE Trans. Information Theory, 44(4), 1369-1387, 1998.
  • A. E. Brouwer, Tables of linear codes, http://www.win.tue.nl/ aeb/.
  • M. Grassl, http://www.codetables.de.
  • F. J. MacWilliams and N. J. A. Sloane,
  • The Theory of Error-Correcting Codes, North-Holland, Amsterdam 1977.
  • G. Nebe, E. M. Rains, N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
  • V. D. Tonchev, Quantum codes from caps, Discrete Math., 308, 6368-6372, 2008.

The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes

Yıl 2014, Cilt: 1 Sayı: 1, 13 - 17, 01.03.2014
https://doi.org/10.13069/jacodesmath.25090

Öz

The existence of a quantum $[[28,12,6]]$ code was one of the few cases for codes of length $n\le 30$ that was left open in the seminal paper by Calderbank, Rains, Shor, and Sloane \cite{CRSS}. The main result of this paper is the construction of a new optimal linear quaternary $[28,20,6]$ code which contains its hermitian dual code and yields an optimal linear quantum $[[28,12,6]]$ code.

Kaynakça

  • W. Bosma, J. Cannon, J, Handbook of Magma Functions, Department of Mathematics, University of Sydney, 1994.
  • A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, Quantum error correction via codes over GF (4), IEEE Trans. Information Theory, 44(4), 1369-1387, 1998.
  • A. E. Brouwer, Tables of linear codes, http://www.win.tue.nl/ aeb/.
  • M. Grassl, http://www.codetables.de.
  • F. J. MacWilliams and N. J. A. Sloane,
  • The Theory of Error-Correcting Codes, North-Holland, Amsterdam 1977.
  • G. Nebe, E. M. Rains, N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
  • V. D. Tonchev, Quantum codes from caps, Discrete Math., 308, 6368-6372, 2008.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Vladimir D. Tonchev

Yayımlanma Tarihi 1 Mart 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 1 Sayı: 1

Kaynak Göster

APA Tonchev, V. D. (2014). The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes. Journal of Algebra Combinatorics Discrete Structures and Applications, 1(1), 13-17. https://doi.org/10.13069/jacodesmath.25090
AMA Tonchev VD. The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes. Journal of Algebra Combinatorics Discrete Structures and Applications. Mart 2014;1(1):13-17. doi:10.13069/jacodesmath.25090
Chicago Tonchev, Vladimir D. “The Existence of Optimal Quaternary [28, 20, 6] and Quantum [[28, 12, 6]] Codes”. Journal of Algebra Combinatorics Discrete Structures and Applications 1, sy. 1 (Mart 2014): 13-17. https://doi.org/10.13069/jacodesmath.25090.
EndNote Tonchev VD (01 Mart 2014) The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes. Journal of Algebra Combinatorics Discrete Structures and Applications 1 1 13–17.
IEEE V. D. Tonchev, “The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 1, sy. 1, ss. 13–17, 2014, doi: 10.13069/jacodesmath.25090.
ISNAD Tonchev, Vladimir D. “The Existence of Optimal Quaternary [28, 20, 6] and Quantum [[28, 12, 6]] Codes”. Journal of Algebra Combinatorics Discrete Structures and Applications 1/1 (Mart 2014), 13-17. https://doi.org/10.13069/jacodesmath.25090.
JAMA Tonchev VD. The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1:13–17.
MLA Tonchev, Vladimir D. “The Existence of Optimal Quaternary [28, 20, 6] and Quantum [[28, 12, 6]] Codes”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 1, sy. 1, 2014, ss. 13-17, doi:10.13069/jacodesmath.25090.
Vancouver Tonchev VD. The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1(1):13-7.