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Generalized Hamming Weights of Irreducible Cyclic Codes

Information Theory 2014-10-13 v1 math.IT

Abstract

The generalized Hamming weight (GHW) dr(C)d_r(C) of linear codes CC is a natural generalization of the minimum Hamming distance d(C)(=d1(C))d(C)(=d_1(C)) and has become one of important research objects in coding theory since Wei's originary work [23] in 1991. In this paper two general formulas on dr(C)d_r(C) for irreducible cyclic codes are presented by using Gauss sums and the weight hierarchy {d1(C),d2(C),,dk(C)}\{d_1(C), d_2(C), \ldots, d_k(C)\} (k=dimC)(k=\dim C) are completely determined for several cases.

Keywords

Cite

@article{arxiv.1410.2702,
  title  = {Generalized Hamming Weights of Irreducible Cyclic Codes},
  author = {Minghui Yang and Jin Li and Keqin Feng and Dongdai Lin},
  journal= {arXiv preprint arXiv:1410.2702},
  year   = {2014}
}
R2 v1 2026-06-22T06:19:07.023Z