TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access A

On a decoding algorithm of mΘ Reed-Muller codes

* ,

* Corresponding author · click or hover a name for details

pp. 341–358Vol. 26Issue 2March 2022DOI: 10.1080/09720529.2021.1920189 Crossmark XML
Received:
01 Sep 2020
Accepted:
05 Jan 2021
Published Online:
14 Nov 2021
Article type:
A
Language:
EN
Article no.:
JDMSC-1308
Pages:
341–358

Abstract

In this paper, we propose an algorithm for decoding for mΘ Reed-Muller codes. Thus, we present first the notion of mΘ spectrum of Reed-Muller codes as in [2]; and we define secondly the notion of mΘ extension of Reed-Muller codes.

Keywords

Subject Classifications

94B6094B75

References

  1. F. Ayissi EtemeLogique et Algèbre de structures mathématiques modales Θ -valentes chrysippiennes. Edition Hermann, Paris2009[Google Scholar]
  2. J. A. Tsimi and G. PemhamΘ spectrum of Reed-Muller codesJournal of Discrete Mathematical Sciences and Cryptography vol. 24, 2021, pp. 1 – 17. doi: https://doi.org/10.1080/09720529.2020.1861781 [Taylor & Francis Online][Google Scholar]
  3. F. Ayissi EtemeAnneau chrysipien Θ -valent, CRAS, Paris 298, série 1, 1984, pp. 1-4[Google Scholar]
  4. F. Ayissi EtemeComplétion chrysipienne d’une algèbre de Lukasiewicz Θ -valent, CRAS, Paris, 299, Série 1(3), 1984, pp. 69-72[Google Scholar]
  5. F. Ayissi EtemeComplétion chrysippienne d’une algèbre de Lukasiewicz Θ -valent, CRAS, Paris, 299, Série 1, 1984, pp.1-4[Google Scholar]
  6. F.A. Eteme and J.A. TsimiA modal Θ -valent approach of the notion of codeJournal of Discrete Mathematical Sciences and Cryptography, vol. 14, October 2011, pp. 445-473. doi: https://doi.org/10.1080/09720529.2011.10698348 [Taylor & Francis Online][Google Scholar]
  7. F. Ayissi EtemeSpectre Θ -valent d’un ach Θ et représentation intrinsèque d’ach Θ, Revue Romaine de Mathématiques Pures et Appliquées, Bucarest, Roumanie, 1992[Google Scholar]
  8. Papini O. and Wolfmann J.Algèbre discrete et codes correcteurs, Springer-VerlagMathématiques et Application, No. 20, 1995[Google Scholar]
  9. F.A. Eteme and J.A. TsimimΘ approach of the algebraic theory of linear codesJournal of Discrete Mathematical Sciences and Cryptography, vol.14 (2011), No. 6, pp. 559-581 doi: https://doi.org/10.1080/09720529.2011.10698356 [Taylor & Francis Online][Google Scholar]
  10. F. Ayissi Eteme, Chrysippian mΘ valent introducing pure and applied mathematics, LAP Lambert Academic Publishing2015Deutschland, Germany[Google Scholar]
  11. F. Ayissi Eteme and J.A. TsimiThe mΘ cyclic codes on a mΘ field2016, pp 313-344, Volume 25 Issue3 (International Journal of Mathematics, Game theory and algebra). [Google Scholar]
  12. Mercier D.J.L’algèbre dans la correction des erreurs, A.P.M.E.P., Bulletin n°415, 1998, pp. 173-191 [Google Scholar]
  13. R.E. BlahutTheory and Practice of error control codes Addison-Wesley1983[Google Scholar]
  14. S. Lin and D.J. Costello Jr., Error control coding Fundamentals and Applications. Prentice Hall1983[Google Scholar]
Views: 111Downloads: 2Citations: 0