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Year 2017, Volume: 5 Issue: 2, 69 - 75, 30.10.2017

İsmail Aydogdu Abidin Kaya

https://doi.org/10.36753/mathenot.421738
Cited By: 1

Abstract

References

  • [1] Abualrub, T., Siap, I. and Aydin, N.,Z2Z4-additive cyclic codes, IEEE Trans. Inform. Theory, Vol. 60, No. 3, pp. 1508-1514, Mar. 2014.
  • [2] Abualrub, T. and Siap, I., Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2, Designs Codes and Cryptography. Vol.42, No.3, 273-287(2007).
  • [3] Aydogdu, I. and Siap, I., The Structure of Z2Z2s−Additive Codes: Bounds on the minimum distance, Applied Mathematics and Information Sciences,7, (6), 2271-2278, 2013.
  • [4] Aydogdu, I., Abualrub, T. and Siap, I., On Z2Z2[u]−additive codes, International Journal of Computer Mathematics, vol.92, no. 9, pp. 1806-1814, 2015.
  • [5] Bonnecaze, A. and Udaya, P., Cyclic codes and self-dual codes over F2 + uF2, IEEE Trans. Inform. Theory. Vol.45, No.4, 1250-1255, 1999.
  • [6] Borges, J., Fernández-Córdoba, C., Pujol, J., Rifà, J. and Villanueva, M., Z2Z4-linear codes: Generator Matrices and Duality, Designs, Codes and Cryptography, 54, (2), 167-179, 2010.
  • [7] J. H. Conway, and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, Vol. 36, No. 6, pp. 1319–1333, 1990.
  • [8] S.T. Dougherty, P. Gaborit, M. Harada and P. Solé, Type II codes over F2 + uF2, IEEE Trans. Inform. Theory, Vol. 45, pp.32-45, 1999.
  • [9] Grassl, M., Code tables: Bounds on the parameters of various types of codes, Online database. Available at http://www.codetables.de/
  • [10] Kaya, A. Yildiz, B., New extremal binary self-dual codes of length 68, J. Algebra Comb. Discrete Appl., Vol. 1, No. 1, 29-39, 2014.
  • [11] Qian, J.F., Zhang, L.N. and Zhu, S.X., (1 + u)-constacyclic and cyclic codes over F2 + uF2, Applied Math. Letters 19 (2006) 820-823.

On Self-Dual Z2Z2[u]-linear Codes

Year 2017, Volume: 5 Issue: 2, 69 - 75, 30.10.2017

İsmail Aydogdu Abidin Kaya

https://doi.org/10.36753/mathenot.421738
Cited By: 1

Abstract


Keywords

Self-dual codes type I codes type II codes Z2Z2 u -linear codes

References

  • [1] Abualrub, T., Siap, I. and Aydin, N.,Z2Z4-additive cyclic codes, IEEE Trans. Inform. Theory, Vol. 60, No. 3, pp. 1508-1514, Mar. 2014.
  • [2] Abualrub, T. and Siap, I., Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2, Designs Codes and Cryptography. Vol.42, No.3, 273-287(2007).
  • [3] Aydogdu, I. and Siap, I., The Structure of Z2Z2s−Additive Codes: Bounds on the minimum distance, Applied Mathematics and Information Sciences,7, (6), 2271-2278, 2013.
  • [4] Aydogdu, I., Abualrub, T. and Siap, I., On Z2Z2[u]−additive codes, International Journal of Computer Mathematics, vol.92, no. 9, pp. 1806-1814, 2015.
  • [5] Bonnecaze, A. and Udaya, P., Cyclic codes and self-dual codes over F2 + uF2, IEEE Trans. Inform. Theory. Vol.45, No.4, 1250-1255, 1999.
  • [6] Borges, J., Fernández-Córdoba, C., Pujol, J., Rifà, J. and Villanueva, M., Z2Z4-linear codes: Generator Matrices and Duality, Designs, Codes and Cryptography, 54, (2), 167-179, 2010.
  • [7] J. H. Conway, and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, Vol. 36, No. 6, pp. 1319–1333, 1990.
  • [8] S.T. Dougherty, P. Gaborit, M. Harada and P. Solé, Type II codes over F2 + uF2, IEEE Trans. Inform. Theory, Vol. 45, pp.32-45, 1999.
  • [9] Grassl, M., Code tables: Bounds on the parameters of various types of codes, Online database. Available at http://www.codetables.de/
  • [10] Kaya, A. Yildiz, B., New extremal binary self-dual codes of length 68, J. Algebra Comb. Discrete Appl., Vol. 1, No. 1, 29-39, 2014.
  • [11] Qian, J.F., Zhang, L.N. and Zhu, S.X., (1 + u)-constacyclic and cyclic codes over F2 + uF2, Applied Math. Letters 19 (2006) 820-823.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İsmail Aydogdu This is me

Abidin Kaya This is me

Publication Date October 30, 2017
Submission Date October 17, 2016
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Aydogdu, İ., & Kaya, A. (2017). On Self-Dual Z2Z2[u]-linear Codes. Mathematical Sciences and Applications E-Notes, 5(2), 69-75. https://doi.org/10.36753/mathenot.421738
AMA Aydogdu İ, Kaya A. On Self-Dual Z2Z2[u]-linear Codes. Math. Sci. Appl. E-Notes. October 2017;5(2):69-75. doi:10.36753/mathenot.421738
Chicago Aydogdu, İsmail, and Abidin Kaya. “On Self-Dual Z2Z2[u]-Linear Codes”. Mathematical Sciences and Applications E-Notes 5, no. 2 (October 2017): 69-75. https://doi.org/10.36753/mathenot.421738.
EndNote Aydogdu İ, Kaya A (October 1, 2017) On Self-Dual Z2Z2[u]-linear Codes. Mathematical Sciences and Applications E-Notes 5 2 69–75.
IEEE İ. Aydogdu and A. Kaya, “On Self-Dual Z2Z2[u]-linear Codes”, Math. Sci. Appl. E-Notes, vol. 5, no. 2, pp. 69–75, 2017, doi: 10.36753/mathenot.421738.
ISNAD Aydogdu, İsmail - Kaya, Abidin. “On Self-Dual Z2Z2[u]-Linear Codes”. Mathematical Sciences and Applications E-Notes 5/2 (October 2017), 69-75. https://doi.org/10.36753/mathenot.421738.
JAMA Aydogdu İ, Kaya A. On Self-Dual Z2Z2[u]-linear Codes. Math. Sci. Appl. E-Notes. 2017;5:69–75.
MLA Aydogdu, İsmail and Abidin Kaya. “On Self-Dual Z2Z2[u]-Linear Codes”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 2, 2017, pp. 69-75, doi:10.36753/mathenot.421738.
Vancouver Aydogdu İ, Kaya A. On Self-Dual Z2Z2[u]-linear Codes. Math. Sci. Appl. E-Notes. 2017;5(2):69-75.

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