In this paper, a study of a sufficient condition on the optimality of a decoded codeword of soft-decision decodings for binary linear codes is shown for a quantized case. A typical uniform 4-level quantizer for soft-decision decodings is employed for the analysis. Simulation results on the (64,42,8) Reed-Muller code indicates that the condition is effective for SN ratios at 3[dB] or higher for any iterative style optimum decodings.