Tensor codes for the rank metric

Linear spaces of n/spl times/n/spl times/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 /spl mu/. Such linear spaces can recover any n/spl times/n/spl times/n error tensor of rank /spl les/ (/spl mu/-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 /spl mu//spl les/2n+1, and constructions are provided for /spl mu//spl les/2n-1 with redundancy which is linear in n. These constructions can be generalized to spaces of n/spl times/n/spl times/.../spl times/n hyper-arrays.