Binary frames with prescribed dot products and frame operator

Abstract

This paper extends three results from classical finite frame theory over real or 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 binary analog of the characterization of dual frames with given inner products and of general frames with prescribed norms and frame operator.