%0 Journal Article %T Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Momenaee Kermani, H. %A Ashenab, M. %D 2017 %\ 12/30/2017 %V 43 %N 7 %P 2483-2493 %! Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces %K Space-time coding‎ %K ‎linear dispersion‎ %K ‎full diversity‎ %K ‎full rank‎ %R %X ‎In wireless communication systems‎, ‎space-time codes are applied to encode data when multiple antennas are used in the receiver and transmitter‎. ‎The concept of diversity is very crucial in designing space-time codes‎. ‎In this paper‎, ‎using the equivalent definition of full diversity space-time codes‎, ‎we first characterize all real and complex $2\times 2$ rate one linear dispersion space-time block codes that are full diversity‎. ‎This characterization is used to construct full diversity codes which are not derived from Alamouti scheme‎. ‎Then‎, ‎we apply our results to characterize all real subspaces of $M_{2}(\mathbb{C})$ and $M_{2}(\mathbb{R})$ whose nonzero elements are invertible‎. ‎Finally‎, ‎for any natural number $n>1$‎, ‎we construct infinitely many inequivalent subspaces of $M_{n}(\mathbb{C})$ whose nonzero elements are invertible. %U http://bims.iranjournals.ir/article_1174_53974d9400ee9e1f4349ffd74f245181.pdf