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

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}.

arXiv comment11 pages, 2 tables