DOI QR코드

DOI QR Code

COMPLETE WEIGHT ENUMERATORS OF SOME CLASSES OF LINEAR CODES WITH A FEW WEIGHTS

  • Liu, Yiwei (Department of Mathematics Beijing Institute of Technology) ;
  • Liu, Zihui (Beijing Key Laboratory on MCAACI)
  • Received : 2017.01.26
  • Accepted : 2017.08.17
  • Published : 2018.05.31

Abstract

By choosing defining set properly, several classes of linear codes with a few weights over the finite field ${\mathbb{F}}_p$ are constructed for an odd prime p, and the complete weight enumerators of these classes of codes are determined.

Keywords

References

  1. J. Ahn, D. Ka, and C. Li, Complete weight enumerators of a class of linear codes, Des. Codes Cryptogr. 83 (2017), no. 1, 83-99. https://doi.org/10.1007/s10623-016-0205-8
  2. I. F. Blake and K. Kith, On the complete weight enumerator of Reed-Solomon codes, SIAM J. Discrete Math. 4 (1991), no. 2, 164-171. https://doi.org/10.1137/0404016
  3. C. Ding, Linear codes from some 2-designs, IEEE Trans. Inform. Theory 61 (2015), no. 6, 3265-3275. https://doi.org/10.1109/TIT.2015.2420118
  4. C. Ding, T. Helleseth, T. Klve, and X. Wang, A generic construction of Cartesian authentication codes, IEEE Trans. Inform. Theory 53 (2007), no. 6, 2229-2235. https://doi.org/10.1109/TIT.2007.896872
  5. K. Ding and C. Ding, A class of two-weight and three-weight codes and their applications in secret sharing, IEEE Trans. Inform. Theory 61 (2015), no. 11, 5835-5842. https://doi.org/10.1109/TIT.2015.2473861
  6. W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, Cambridge, 2003.
  7. C. Li and Q. Yue, Weight distributions of two classes of cyclic codes with respect to two distinct order elements, IEEE Trans. Inform. Theory 60 (2014), no. 1, 296-303. https://doi.org/10.1109/TIT.2013.2287211
  8. R. Lidl and H. Niederreiter, Finite Fields, second edition, Encyclopedia of Mathematics and its Applications, 20, Cambridge University Press, Cambridge, 1997.
  9. C. Tang, N. Li, Y. Qi, Z. Zhou, and T. Helleseth, Linear codes with two or three weights from weakly regular bent functions, IEEE Trans. Inform. Theory 62 (2016), no. 3, 1166-1176. https://doi.org/10.1109/TIT.2016.2518678
  10. C. Tang, Y. Qi, and D. Huang, Two-weight and three-weight linear codes from square functions, IEEE Communications Letters 20 (2016), no. 1, 29-32. https://doi.org/10.1109/LCOMM.2015.2497344
  11. S. Yang and Z.-A. Yao, Complete weight enumerators of a family of three-weight linear codes, Des. Codes Cryptogr. 82 (2017), no. 3, 663-674. https://doi.org/10.1007/s10623-016-0191-x