We study properties of the meet of two rational codes X and Y, defined
as the base of the free monoid X boolean AND Y*. We first give sever
al examples of rational maximal codes X and Y such that their meet is
no longer a maximal code. We give a combinatorial characterization of
the rational maximal codes X, Y for which the meet is a maximal code.
We also show that any rational (maximal or not) code is the meet of tw
o rational maximal codes.