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Efficiently repairing algebraic geometry codes. (arXiv:1710.01874v1 [cs.IT])
来源于:arXiv
Minimum storage regenerating codes have minimum storage of data in each node
and therefore are maximal distance separable (MDS for short) codes. Thus, the
number of nodes is upper bounded by $2^{\fb}$, where $\fb$ is the bits of data
stored in each node. From both theoretical and practical points of view (see
the details in Section 1), it is natural to consider regenerating codes that
nearly have minimum storage of data, and meanwhile the number of nodes is
unbounded. One of the candidates for such regenerating codes is an algebraic
geometry code. In this paper, we generalize the repairing algorithm of
Reed-Solomon codes given in \cite[STOC2016]{GW16} to algebraic geometry codes
and present an efficient repairing algorithm for arbitrary one-point algebraic
geometry codes. By applying our repairing algorithm to the one-point algebraic
geometry codes based on the Garcia-Stichtenoth tower, one can repair a code of
rate $1-\Ge$ and length $n$ over $\F_{q}$ with bandwidth $(n-1)(1-\Gt)\log 查看全文>>