  Past few years have seen an extensive use of RAM chips with wide I/O data
(e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly
vulnerable to a special type of byte error, called an $m$-spotty byte error,
which can be effectively detected or corrected using byte error-control codes.
The MacWilliams identity provides the relationship between the weight
distribution of a code and that of its dual. The main purpose of this paper is
to present a version of the MacWilliams identity for $m$-spotty weight
enumerators over
$\mathbbm{F}_{2}+u\mathbbm{F}_{2}+\cdots+u^{m-1}\mathbbm{F}_{2}$ (shortly
$R_{u, m, 2}$).
