Abstract
The MSCR (minimum storage cooperative regenerating) code is an important variation of regenerating codes for repairing multiple node failures in a cooperative way and retaining the minimum storage. However, explicit constructions of MSCR codes for all parameters were not developed untill Ye&Barg's recent work. Here we present another explicit construction of MSCR codes for all parameters. Specifically, we design an (n, k) MDS code that can cooperatively repair any h (2 ≤ h ≤ n - k) erasures from any d (k ≤ d ≤ n - h) helper nodes. The superiority of our code to Ye&Barg's is three fold: (1) Our code additionally has the optimal access property, i.e., the amount of data accessed at each helper node meets a lower bound on this quantity; (2) The subpacketization level is reduced by a factor of (d - k) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(h-1)</sup> ( <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ); (3) Our code is built over a smaller field F with |F| ≥ n + d - k, compared to Ye&Barg's requirement |F| ≥ (d - k + 1)n.
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