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With the rapid progress of the capacity and slow pace of the speed/MTTF of hard disks, and increasing size of storage systems, the reliability and availability of storage systems become more and more serious. This paper discusses the method of constructing double- and triple-erasure-correcting codes via combining mirroring and parity approaches in details, and presents a double-erasure code MPDC and a triple-erasure code MPPDC based on one-factorizations of complete graphs. The two codes are simple, easy to implement, and have no disk number limitation. They achieve perfect fault-free load balance and approximately optimal reconstruction load balance. The simulation results show that, compared with other double- and triple-erasure codes, MPDC and MPPDC have comparative light-load and moderate-load performance and better heavy-load performance in fault-free mode. Because parity declustering is used, the two codes are far superior to the other double- and triple-erasure codes in degraded- and reconstruction-mode performance.