# Binary frames with prescribed dot products and frame operator

## TL;DR

This paper extends classical finite frame theory to binary frames over ${
m Z}_2^d$, establishing analogs of fundamental inequalities and characterizations of dual and general frames without inner products.

## Contribution

It introduces new binary frame theory results, including analogs of fundamental inequalities and frame characterizations, for vector spaces over ${
m Z}_2^d$.

## Key findings

- Established a binary analog of the fundamental inequality for tight frames.
- Characterized dual frames with prescribed inner products in binary frame setting.
- Described general frames with prescribed norms and frame operators in binary context.

## 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.