Minimum Distance of New Generalizations of the Punctured Binary Reed-Muller Codes

Liqin Hu; Keqin Feng

Minimum Distance of New Generalizations of the Punctured Binary Reed-Muller Codes

Information Theory 2018-05-29 v1 math.IT

Authors: Liqin Hu , Keqin Feng

Abstract

Motivated by applications in combinatorial design theory and constructing LCD codes, C. Ding et al \cite{DLX} introduced cyclic codes $\mho(q,m,h)$ and $\bar\mho(q,m,h)$ over $\mathbb{F}_q$ as new generalization and version of the punctured binary Reed-Muller codes. In this paper, we show several new results on minimum distance of $\mho(q,m,h)$ and $\bar\mho(q,m,h)$ which are generalization or improvement of previous results given in \cite{DLX}.

Keywords

cyclic codes punctured binary reed-muller codes minimum distance lcd codes finite fields combinatorial designs

Cite

@article{arxiv.1805.10562,
  title  = {Minimum Distance of New Generalizations of the Punctured Binary Reed-Muller Codes},
  author = {Liqin Hu and Keqin Feng},
  journal= {arXiv preprint arXiv:1805.10562},
  year   = {2018}
}

Comments

11 pages, 2 tables

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