  The well known Plotkin construction is, in the current paper, generalized and
used to yield new families of Z2Z4-additive codes, whose length, dimension as
well as minimum distance are studied. These new constructions enable us to
obtain families of Z2Z4-additive codes such that, under the Gray map, the
corresponding binary codes have the same parameters and properties as the usual
binary linear Reed-Muller codes. Moreover, the first family is the usual binary
linear Reed-Muller family.
