On the Composition of Secret Sharing Schemes Related to Codes

In this paper we construct a subclass of the composite access structure introduced in [9] 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 [9]. 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.