Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is odd about binary Parseval frames?   This paper examines the construction and properties of binary Parseval
frames. We address two questions: When does a binary Parseval frame have a
complementary Parseval frame? Which binary symmetric idempotent matrices are
Gram matrices of binary Parseval frames? In contrast to the case of real or
complex Parseval frames, the answer to these questions is not always
affirmative. The key to our understanding comes from an algorithm that
constructs binary orthonormal sequences that span a given subspace, whenever
possible. Special regard is given to binary frames whose Gram matrices are
circulants.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat