Tensors, matchings and codes

We exploit the structure of the critical orbital sets of symmetry classes of tensors associated to sign uniform partitions and we establish new connections between symmetry classes of tensors, matchings on bipartite graphs and coding theory. In particular, we prove that the orthogonal dimension of the critical orbital sets associated to single hook partitions λ=(w,1n-w) equals the value of the coding theoretic function A(n,4,w). When w=2 we reobtain this number as the independence number of the Dynkin diagram An-1.