  In 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.
