Momenaee Kermani, H., Ashenab, M. (2017). Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces. Bulletin of the Iranian Mathematical Society, 43(7), 2483-2493.

H. Momenaee Kermani; M. Ashenab. "Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces". Bulletin of the Iranian Mathematical Society, 43, 7, 2017, 2483-2493.

Momenaee Kermani, H., Ashenab, M. (2017). 'Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces', Bulletin of the Iranian Mathematical Society, 43(7), pp. 2483-2493.

Momenaee Kermani, H., Ashenab, M. Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces. Bulletin of the Iranian Mathematical Society, 2017; 43(7): 2483-2493.

Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces

^{1}Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

^{2}Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

^{3}Young Researchers Society, Shahid Bahonar University of Kerman, Kerman, Iran.

Receive Date: 28 January 2017,
Revise Date: 11 October 2017,
Accept Date: 13 October 2017

Abstract

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.

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