Technical Report CS0860

TR#:CS0860
Class:CS
Title: TENSOR CODES FOR THE RANK METRIC.
Authors: Ron M. Roth
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Abstract: Linear spaces of $n \times n \times n$ tensors over finite fields are investigated where the rank of every nonzero tensor in the space is bounded from below by a prescribed number $\mu$. Such linear paces can recover any $n \times n \times n$ error tensor of rank $ \leq(\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 $\mu \leq 2n+1$, and constructions are provided for $\mu \leq 2n-1$ with redundancy which is linear in $n$. These constructions can be generalized to spaces of $n \times n \times \cdots \times n$ hyper-arrays.
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