English

New MDS or near MDS self-dual codes over finite fields

Information Theory 2016-09-16 v1 math.IT

Abstract

The study of MDS self-dual codes has attracted lots of attention in recent years. There are many papers on determining existence of qq-ary MDS self-dual codes for various lengths. There are not existence of qq-ary MDS self-dual codes of some lengths, even these lengths <q< q. We generalize MDS Euclidean self-dual codes to near MDS Euclidean self-dual codes and near MDS isodual codes. And we obtain many new near MDS isodual codes from extended negacyclic duadic codes and we obtain many new MDS Euclidean self-dual codes from MDS Euclidean self-dual codes. We generalize MDS Hermitian self-dual codes to near MDS Hermitian self-dual codes. We obtain near MDS Hermitian self-dual codes from extended negacyclic duadic codes and from MDS Hermitian self-dual codes.

Keywords

Cite

@article{arxiv.1609.04602,
  title  = {New MDS or near MDS self-dual codes over finite fields},
  author = {Hongxi Tong and Xiaoqing Wang},
  journal= {arXiv preprint arXiv:1609.04602},
  year   = {2016}
}

Comments

12 pages