Tensor codes for the rank metric

Linear spaces of n×n×n tensors over finite fields are investigated where the rank of every nonzero tensor in the space is bounded from below by a prescribed number μ. Such linear spaces can recover any n×n×n error tensor of rank ⩽ (μ-1)/2, and, as such, they can be used to correct three-way crisscross errors. Bounds on the dimensions of such spaces are given for μ⩽2n+1, and constructions are provided for μ⩽2n-1 with redundancy which is linear in n. These constructions can be generalized to spaces of n×n×...×n hyper-arrays