ZRM codes

Quaternary ZRM(r, m)codes were defined so that their binary images, via Gray map, are Reed-Muller codes for some specific values of r. In the literature, two different definitions of such codes can be found. They will be denoted ZRM(r,m) and ZRM - (r,m) codes. In this correspondence, we show that both definitions are equivalent exactly for those values of r such that their binary images are Reed-Muller codes. Moreover, we prove that, for all r, these binary images are linear codes in the case of ZRM - (r,m), but they are not if we use the definition of ZRM - (r,m). In this last case, we compute the rank and the dimension of the kernel of these codes. © 2008 IEEE.