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We show that the problem of deciding whether a given Euclidean lattice L hasan orthonormal basis is in NP and co-NP. Since this is equivalent to sayingthat L is isomorphic to the standard integer lattice, this problem is a specialform of the Lattice Isomorphism Problem, which is known to be in the complexityclass SZK.

Deciding whether a Lattice has an Orthonormal Basis is in co-NP