A claimed explicit matrix factorization using roots of unity would match the best known error bound for private continual counting, but the construction as written does not multiply back to the target matrix.
A smooth binary mechanism for efficient private continual observation
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Improved Differentially Private Continual Observation Using Group Algebra
A claimed explicit matrix factorization using roots of unity would match the best known error bound for private continual counting, but the construction as written does not multiply back to the target matrix.