Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DUADIC CODES OVER FINITE LOCAL RINGS

  • Received : 2020.03.06
  • Accepted : 2021.12.06
  • Published : 2022.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce duadic codes over finite local rings and concentrate on quadratic residue codes. We study their properties and give the comprehensive method for the computing the unique idempotent generator of quadratic residue codes.

Keywords

Acknowledgement

The authors would like to thank the referees for carefully reading the manuscript and for their valuable comments and suggestions which improved the exposition of the paper.

References

  1. M. H. Chiu, S. T. Yau, and Y. Yu, ℤ8-cyclic codes and quadratic residue codes, Adv. Math. Commun. 11 (2017), no. 1, 99-114. https://doi.org/10.3934/amc.2017005
  2. W. C. Huffman and V. Pless, Fundamentals of error-correcting codes, Cambridge University Press, Cambridge, 2003. https://doi.org/10.1017/CBO9780511807077
  3. J. S. Leon, J. M. Masley, and V. Pless, Duadic codes, IEEE Trans. Inform. Theory 30 (1984), no. 5, 709-714. https://doi.org/10.1109/TIT.1984.1056944
  4. B. R. McDonald, Finite rings with identity, Pure and Applied Mathematics, Vol. 28, Marcel Dekker, Inc., New York, 1974.
  5. G. H. Norton and A. Salagean, On the structure of linear and cyclic codes over a finite chain ring, Appl. Algebra Engrg. Comm. Comput. 10 (2000), no. 6, 489-506. https://doi.org/10.1007/PL00012382
  6. V. S. Pless and Z. Qian, Cyclic codes and quadratic residue codes over Z4, IEEE Trans. Inform. Theory 42 (1996), no. 5, 1594-1600. https://doi.org/10.1109/18.532906
  7. R. Y. Sharp, Steps in Commutative Algebra, second edition, London Mathematical Society Student Texts, 51, Cambridge University Press, Cambridge, 2000.
  8. B. Taeri, Quadratic residue codes over ℤ9, J. Korean Math. Soc. 46 (2009), no. 1, 13-30. https://doi.org/10.4134/JKMS.2009.46.1.013