Asymptotic solution of the Turán problem for some hypergraphs

Taking an ordinary graphL ² and replacing each of its vertices by a group ofr/2 vertices (r is even), we get anr-uniform hypergraphL′. In the casex(L ²)=2^m+1, we solve asymptotically the Turán problem forL′. Ifx(L ²)#2^m+1, the upper bound is still valid but proper constructions are not known.