Explicit Constructions of High-Rate MSR Codes with Optimal Access Property over Small Finite Fields

Up to now, many (k + r, k, N) minimum-storage regenerating (MSR) codes with k information nodes, r parity nodes, and node capacity N have been proposed. However, most of them are constructed over a relatively large finite field. In this paper, we propose three high-rate MSR codes over small finite fields. First, the new MSR code C1with the optimal access property for all nodes is constructed over small finite field Fq, for example q = 3 for even r or q ≥ r + 1 for odd r, which is much smaller than that of the known one given by Ye and Barg. Further, considering to reduce the node capacity, another new MSR code C2over Fqwith q ≥ r + 2 is generated based on C1, which can effectively reduce the node capacity of C1by a factor of rr-1. However, only the first k nodes of C2have the optimal access property. Therefore, the new MSR code C3over Fqwith q ≥ r + 2 which has the optimal access property for all nodes is proposed by modifying C2. Notably, in contrast to C1, the node capacity of C3is decreased by a factor of rr-2.