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To reduce the complexity of algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes, re-encoding and coordinate transformation can be applied. For an (n, k) code, the re-encoding was implemented as applying erasure decoding to the k most reliable code positions previously. Such re-encoding can occupy a significant part of the overall decoder area. In this brief, we propose to choose the first k positions and implement the re-encoding in the low-complexity Chase (LCC) ASD algorithm by systematic encoding, which can be done by simple constant multipliers. Moreover, novel schemes are developed to modify the following interpolation and codeword recovery steps in the case that systematic symbols need to be flipped to form the test vectors in the LCC decoding. Without any performance loss, the proposed schemes can lead to 15.5% higher efficiency in terms of throughput-over-area ratio in the LCC decoder with eight test vectors for a (255, 239) RS code over GF(28).