Generalization of Rashmi-Shah-Kumar Minimum-Storage-Regenerating Codes

In this paper, we propose a generalized version of the Rashmi-Shah-Kumar Minimum-Storage-Regenerating(RSKMSR) codes based on the product-matrix framework. For any (n, k, d) such that d ≥ 2k − 2 and d ≤ 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 {l, l} secure codes based on the generalized RSK-MSR codes can be obtained by applying the construction method of {l, l} 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 {l = k, l = 0} secure code.