This paper extends three results from classical finite frame theory over realor complex numbers to binary frames for the vector space ${\mathbb Z}_2^d$.Without the notion of inner products or order, we provide an analog of the"fundamental inequality" of tight frames. In addition, we prove the binaryanalog of the characterization of dual frames with given inner products and ofgeneral frames with prescribed norms and frame operator.
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机译：本文将经典有限框架理论中关于实数复数的三个结果扩展到向量空间$ {\ mathbb Z} _2 ^ d $的二元框架。在没有内积或阶的概念的情况下，我们提供了“基本不等式”的类似物紧框架。此外，我们证明了具有给定内积的双重框架和具有规定范数和框架算子的一般框架的表征的二元模拟。
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