English

Optimal Ternary Cyclic Codes with Minimum Distance Four and Five

Information Theory 2013-09-06 v1 math.IT

Abstract

Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first family of cyclic codes has parameters [3m1,3m12m,4][3^m-1, 3^m-1-2m, 4] and contains a class of conjectured cyclic codes and several new classes of optimal cyclic codes. The second family of cyclic codes has parameters [3m1,3m22m,5][3^m-1, 3^m-2-2m, 5] and contains a number of classes of cyclic codes that are obtained from perfect nonlinear functions over \fthreem\fthreem, where m>1m>1 and is a positive integer.

Keywords

Cite

@article{arxiv.1309.1218,
  title  = {Optimal Ternary Cyclic Codes with Minimum Distance Four and Five},
  author = {Nian Li and Chunlei Li and Tor Helleseth and Cunsheng Ding and Xiaohu Tang},
  journal= {arXiv preprint arXiv:1309.1218},
  year   = {2013}
}
R2 v1 2026-06-22T01:21:06.500Z