Advertisement

Designs, Codes and Cryptography

, Volume 62, Issue 1, pp 31–42 | Cite as

New MDS self-dual codes over finite fields

  • Kenza GuendaEmail author
Article

Abstract

In this paper we construct MDS Euclidean and Hermitian self-dual codes which are extended cyclic duadic codes or negacyclic codes. We also construct Euclidean self-dual codes which are extended negacyclic codes. Based on these constructions, a large number of new MDS self-dual codes are given with parameters for which self-dual codes were not previously known to exist.

Keywords

Self-dual codes MDS codes Cyclic codes Negacyclic codes 

Mathematics Subject Classification (2000)

94B05 94B15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aydin N., Siap I., Ray-Chaudhuri D.J.: The structure of 1-generator quasi-twisted codes and new linear codes. Des. Codes Cryptogr. 24(3), 313–326 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Blackford T.: Negacyclic duadic codes. Finite Fields Appl. 14(4), 930–943 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Betsumiya K., Georgiou S., Gulliver T.A., Harada M., Koukouvinos C.: On self-dual codes over some prime fields. Disc. Math. 262, 37–58 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Demazure M.: Cours D’Algèbre: Primalité. Divisibilité. Codes. Cassini, Paris (1997).Google Scholar
  5. 5.
    Dicuangco L., Moree P., Solé P.: The lengths of hermitian self-dual extended duadic codes. J. Pure Appl. Algebra 209(1), 223–237 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Guenda K.: Quantum duadic and affine invariant codes. Int. J. Quantum Inf. 7(1), 373–384 (2009)CrossRefzbMATHGoogle Scholar
  7. 7.
    Gulliver T.A., Grassl M.: On self-dual MDS codes. In: Proceedings of IEEE International Symposium Information Theory, Toronto, Canada, July (2008).Google Scholar
  8. 8.
    Gulliver T.A., Harada M.: MDS self-dual codes of lengths 16 and 18. Int. J. Inform. Coding Theory 1(2), 208–213 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Dinh H.Q., Lopez-Permount S.R.: Cyclic and negacyclic codes over finite chain rings. IEEE. Trans. Inform. Theory 50(8), 1728–1744 (2004)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Hill R.: An extension theorem for linear codes. Des. Codes Cryptogr. 17(1–3), 151–157 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Huffman W.C., Pless V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  12. 12.
    Kotsireas I.S., Koukouvinos C., Simos D.: MDS and near-MDS self-dual codes over large prime fields. Advan. Math Commun. 3(4), 349–361 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Krishna A., Sarwate D.V.: Pseudo-cyclic maximum-distance-seperable codes. IEEE Trans. Inform. Theory 36(4), 880–884 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. Elsevier, North-Holland (1977)zbMATHGoogle Scholar
  15. 15.
    Smid M.H.M.: Duadic codes. IEEE. Trans. Inform. Theory 33(3), 432–433 (1983)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of MathematicsUSTHB, University of Sciences and Technology of AlgiersAlgiersAlgeria

Personalised recommendations