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29 March 2024
 
  » arxiv » 1309.6701

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Generalization of Rashmi-Shah-Kumar Minimum-Storage-Regenerating Codes
Masazumi Kurihara ; Hidenori Kuwakado ;
Date 26 Sep 2013
AbstractIn this paper, we propose a generalized version of the Rashmi-Shah-Kumar Minimum-Storage-Regenerating(RSK-MSR) codes based on the product-matrix framework. For any $(n,k,d)$ such that $d geq 2k-2$ and $d leq n-1$, we can directly construct an $(n,k,d)$ MSR code without constructing a larger MSR code and shortening of the larger MSR code. As a result, the size of a finite field over which the proposed code is defined is smaller than or equal to the size of a finite field over which the RSK-MSR code is defined. In addition, the ${ell,ell’}$ secure codes based on the generalized RSK-MSR codes can be obtained by applying the construction method of ${ell,ell’}$ secure codes proposed by Shah, Rashmi and Kumar. Furthermore, the message matrix of the $(n,k,d)$ generalized RSK-MSR code is derived from that of the RSK-MSR code by using the construction method of the ${ell=k,ell’=0}$ secure code.
Source arXiv, 1309.6701
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