A $2\times 2$ lattice space-time code of the highest rank
Shichun Yang, Bo He, Alain Togbé · Proceedings of the American Mathematical Society · 2009
For all previous constructions of $2\times 2$ lattice space-time codes with a positive diversity product, the rank $r(2)$ was such that $r(2)\leq 4$. An example of a $2\times 2$ lattice space-time code of rank $5$ with a positive diversity product was given by Xing and Li. In this paper, we give an example of a $2\times 2$ lattice space-time code of rank $8$ with a positive diversity product. This gives an answer to the open problem set by Xing and Li.