  In this paper we construct a subclass of the composite access structure
introduced by Mart\'inez et al. based on schemes realizing the structure given
by the set of codewords of minimal support of linear codes. This class enlarges
the iterated threshold class studied in the same paper. Furthermore all the
schemes on this paper are ideal (in fact they allow a vector space
construction) and we arrived to give a partial answer to a conjecture stated in
the above paper. Finally, as a corollary we proof that all the monotone access
structures based on all the minimal supports of a code can be realized by a
vector space construction.
