TR#: | CS0860 |

Class: | CS |

Title: | TENSOR CODES FOR THE RANK METRIC. |

Authors: | Ron M. Roth |

Not Available | |

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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