正交设计与三次二元函数
Orthogonal Designs and a Cubic Binary Function
摘要：
正交设计是在用于无线传输的空时分组码的构造中使用的基本数学概念。设计有两个重要的参数，速率和解码延迟，该理论的主要问题是构造最大化速率和最小化解码延迟的设计。所有已知的COD构造都是归纳的或算法的。在本文中，我们提出了一个显式的最佳CODs的建设。我们不应用递归程序，直接计算矩阵元素。我们的公式是基于一个三次函数在两个二进制n-向量。在我们以前的工作（通信数学物理，2010，and J. Pure and Appl. Algebra，2011），我们利用这个函数定义了一系列推广经典八元数代数的非结合代数，并得到了Hurwitz-Radon型平方和恒等式.
英文摘要：
Orthogonal 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.
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