Abstract:
Linear spaces of n \Theta n \Theta 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 ��. Such linear paces can recover any n \Theta n \Theta n error tensor of rank (��\Gamma1)=2, and, as such, they can be used to correct three-way crisscross errors. Bounds on the dimensions of such spaces are given for � � 2n+1, and constructions are provided for � � 2n\Gamma1 with redundancy which is linear in n. These constructions can be generalized to spaces of n \Theta n \Theta \Delta \Delta \Delta \Theta n hyper-arrays.
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