Polyphase equiangular tight frames and abelian generalized quadrangles
Polyphase equiangular tight frames and abelian generalized quadrangles
复制标题
多相等角紧框架和阿贝尔广义四边形
DOI：
10.1016/j.acha.2017.11.007
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发表时间：
2016
影响因子：
2.5
通讯作者：
Cody Watson
中科院分区：
文献类型：
--
作者：
M. Fickus;J. Jasper;D. Mixon;Jesse Peterson;Cody Watson
等角紧框架（ETF）是有限维希尔伯特空间中的一种最优线填充。ETF出现在各种应用中，诸如用于无线通信的波形设计、压缩感知、量子信息理论和代数编码理论。在最近的一篇论文中，ETF的签名矩阵构造完全图的阿贝尔距离正则覆盖。我们扩展这项工作，从阿贝尔广义四边形构造ETF合成算子，反之亦然。这就产生了一个新的无限族的复杂ETF，以及一个新的证明存在某些广义四边形。这项工作涉及到设计矩阵的条目是多项式在一个有限的阿贝尔群。因此，它涉及有限滤波器组的多相矩阵的概念。
An equiangular tight frame (ETF) is a type of optimal packing of lines in a finite-dimensional Hilbert space. ETFs arise in various applications, such as waveform design for wireless communication, compressed sensing, quantum information theory and algebraic coding theory. In a recent paper, signature matrices of ETFs were constructed from abelian distance regular covers of complete graphs. We extend this work, constructing ETF synthesis operators from abelian generalized quadrangles, and vice versa. This produces a new infinite family of complex ETFs as well as a new proof of the existence of certain generalized quadrangles. This work involves designing matrices whose entries are polynomials over a finite abelian group. As such, it is related to the concept of a polyphase matrix of a finite filter bank.