On vectors of minimal support in transitive linear spaces

We discuss the minimum distance problem of some transitive linear spaces. A minimal support of vectors in monogenerated coordinate-transitive spaces problem is solved for ones generated by a vector of weight 2. In the case of generating vector of weight 3 some conjectures are provided by computer experiments. Attainable lower bound on the support cardinality with respect to dimension of linear space is obtained. Also a connection between full-rank criterion for vector and tilings of groups is mentioned.