  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}.
