Binary frames, graphs and erasures
Binary frames, graphs and erasures
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二进制框架、图表和擦除
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. Mahoney
中科院分区：
文献类型：
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作者：
B. Bodmann;Bijan Camp;D. Mahoney
本文从框架理论的角度研究了二进制码。二进制Parseval框架具有方便的编码和解码映射。我们的特点是二进制Parseval帧是强大的一个或两个擦除。这些特征给出了相关的格拉姆矩阵和图论条件。我们说明了这些结果与帧的最低维度是强大的一个或两个擦除。此外，我们提出了必要的条件，纠正了大量的擦除。在以前的文件中，我们强调在哪些方面的二元理论不同于理论的框架真实的和复杂的希尔伯特空间。
This paper examines binary codes from a frame-theoretic viewpoint. Binary Parseval frames have convenient encoding and decoding maps. We characterize binary Parseval frames that are robust to one or two erasures. These characterizations are given in terms of the associated Gram matrix and with graph-theoretic conditions. We illustrate these results with frames in lowest dimensions that are robust to one or two erasures. In addition, we present necessary conditions for correcting a larger number of erasures. As in a previous paper, we emphasize in which ways the binary theory differs from the theory of frames for real and complex Hilbert spaces.