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 paces 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.