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Given a generating set of a $\mathbb{Z}$-module $M \subseteq {\mathbb{Z}_k}^n$, is there a known algorithm to compute a generating set of $\{u \in {\mathbb{Z}_k}^n \, : \, \forall v \in M \quad v \cdot u = 0\}$?

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    There is an algorithm for finding a "nice" generating set of $M$ (essentially, [Smith normal form](http://en.wikipedia.org/wiki/Smith_normal_form). I think that from the Smith normal form, it should be straightforward to read off generators for your set.2011-09-06
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    This question has been cross-posted on MathOverflow: ttp://mathoverflow.net/questions?sort=newest2011-09-06

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