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Various techniques have been proposed in the literature to improve erasure code computation efficiency, including optimizing bitmatrix design, optimizing computation schedule, common XOR operation reduction, caching management techniques, and vectorization techniques. These techniques were largely proposed individually previously, and in this work, we seek to use them jointly. In order to accomplish this task, these techniques need to be thoroughly evaluated individually, and their relation better understood. Building on extensive test results, we develop methods to systematically optimize the computation chain together with the underlying bitmatrix. This led to a simple design approach of optimizing the bitmatrix by minimizing a weighted cost function, and also a straightforward erasure coding procedure: use the given bitmatrix to produce the computation schedule, which utilizes both the XOR reduction and caching management techniques, and apply XOR level vectorization. This procedure can provide a better performance than most existing techniques, and even compete against well-known codes such as EVENODD, RDP, and STAR codes. Moreover, the result suggests that vectorizing the XOR operation is a better choice than directly vectorizing finite field operations, not only because of the better encoding throughput, but also its minimal migration efforts onto newer CPUs.