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Sum and direct sum of frame sequences
Linear and Multilinear Algebra, 2013Casazza, Han and Larson characterized various properties of the direct sum of two frame sequences. We add characterizations of other properties and study the relationship between the direct sum and the sum of frame sequences. In particular, we find a necessary and sufficient condition for the sum of two strongly disjoint (orthogonal) frame sequences ...
Yoo Young Koo, Jae Kun Lim
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Summary: The \textit{\(k\)-fold direct sum encoding} of a string \(a\in\{0,1\}^n\) is a function \(f_a\) that takes as input sets \(S\subseteq [n]\) of size \(k\) and outputs \(f_a(S)=\sum_{i\in S}a_i\pmod 2\). In this paper we prove a direct sum testing theorem. We describe a three query test that accepts with probability one any function of the form \
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