Tensor codes for the rank metric

Linear spaces of n×n×n tensors over finite fields are investigated where the rank of any nonzero tensor in the space is at least a prescribed number μ. Such spaces can recover any n×n×n 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