A $2\times 2$ lattice space-time code of the highest rank

For all previous constructions of 2\times 2lattice space-time codes with a positive diversity product, the rank r(2)was such that r(2)\leq 4 An example of a 2\times 2lattice space-time code of rank 5with a positive diversity product was given by Xing and Li. In this paper, we give an example of a 2\times 2lattice space-time code of rank 8with a positive diversity product. This gives an answer to the open problem set by Xing...