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A $ 2\times2$ lattice space-time code of the highest rank


Authors: Shichun Yang, Bo He and Alain Togbé
Journal: Proc. Amer. Math. Soc. 137 (2009), 3601-3607
MSC (2000): Primary 06B99, 15A15; Secondary 11Z05
DOI: https://doi.org/10.1090/S0002-9939-09-10004-7
Published electronically: June 5, 2009
MathSciNet review: 2529866
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Abstract: For all previous constructions of $ 2\times2$ 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\times2$ 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\times2$ 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.


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Additional Information

Shichun Yang
Affiliation: Department of Mathematics, Aba Teachers’ College, Wenchuan, Sichuan, 623000, People’s Republic of China
Email: ysc1020@sina.com

Bo He
Affiliation: Department of Mathematics, Aba Teachers’ College, Wenchuan, Sichuan, 623000, People’s Republic of China
Email: bhe@live.cn

Alain Togbé
Affiliation: Department of Mathematics, Purdue University North Central, 1401 S, U.S. 421, Westville, Indiana 46391
Email: atogbe@pnc.edu

DOI: https://doi.org/10.1090/S0002-9939-09-10004-7
Keywords: Rank, diversity product, lattice
Received by editor(s): February 17, 2009
Published electronically: June 5, 2009
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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