English

The Weight Hierarchy of Some Reducible Cyclic Codes

Information Theory 2015-04-07 v1 Combinatorics math.IT

Abstract

The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we study the GHWs for a family of reducible cyclic codes and obtain the complete weight hierarchy in several cases. This is achieved by extending the idea of \cite{YLFL} into higher dimension and by employing some interesting combinatorial arguments. It shall be noted that these cyclic codes may have arbitrary number of nonzeroes.

Keywords

Cite

@article{arxiv.1504.01274,
  title  = {The Weight Hierarchy of Some Reducible Cyclic Codes},
  author = {Maosheng Xiong and Shuxing Li and Gennian Ge},
  journal= {arXiv preprint arXiv:1504.01274},
  year   = {2015}
}