Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Characterization of $2times 2$ full diversity space-time codes and inequivalent full rank spaces248324931174ENH.Momenaee KermaniDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.M.AshenabDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranYoung Researchers Society, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20170128In 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 $2times 2$ 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.http://bims.iranjournals.ir/article_1174_53974d9400ee9e1f4349ffd74f245181.pdf