If m > n, the O(n)-orbit of a generic m-point binary signal with at least some equal magnitudes is uniquely recoverable from autocorrelation, with an O(m^8) algorithm in R^3 when one magnitude is distinct.
Bandeira, Philippe Rigollet, and Jonathan Weed
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Euclidean distance geometry and the orthogonal beltway problem
If m > n, the O(n)-orbit of a generic m-point binary signal with at least some equal magnitudes is uniquely recoverable from autocorrelation, with an O(m^8) algorithm in R^3 when one magnitude is distinct.