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Orthogonal designs and a cubic binary function

By Sophie Morier-Genoud and Valentin Ovsienko

Abstract

International audienceOrthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is to construct designs maximizing the rate and minimizing the decoding delay. All known constructions of CODs are inductive or algorithmic. In this paper, we present an explicit construction of optimal CODs. We do not apply recurrent procedures and do calculate the matrix elements directly. Our formula is based on a cubic function in two binary n-vectors. In our previous work (Comm. Math. Phys., 2010, and J. Pure and Appl. Algebra, 2011), we used this function to define a series of non-associative algebras generalizing the classical algebra of octonions and to obtain sum of squares identities of Hurwitz-Radon type

Topics: [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]
Publisher: Institute of Electrical and Electronics Engineers
Year: 2013
DOI identifier: 10.1109/TIT.2012.2229335
OAI identifier: oai:HAL:hal-00864648v1
Provided by: Hal-Diderot

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