On the Symmetry Groups of Hypergraphs of Perfect Cwatsets

Cwatsets are subsets of \(\mathbb{Z}^d_2\) which are nearly subgroups and which naturally appear in statistics and coding theory [8]. Each cwatset can be represented by a highly symmetric hypergraph [7]. We introduce and study the symmetry group of the hypergraph and connect it to the corresponding cwatset. We use this connection to establish structure theorems for several classes of cwatsets.