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The forward error correction for 100-Gbit/s optical transport network has received much attention recently. Studies showed that product codes that employ three-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) codes can achieve better performance than other BCH or Reed-Solomon codes. For such codes, the Peterson algorithm can be used to compute the error locator polynomial, and its roots can be found directly using a lookup table (LUT). However, the size of the LUT is quite large for finite fields of high order. In this brief, a novel approach is proposed to reduce the LUT size by at least four times through making use of the properties of the error locator polynomial and normal basis representation of finite field elements. Moreover, hybrid representation of finite field elements is adopted to minimize the complexity of the involved computations. For a (1023, 993) BCH decoder over GF(210), the proposed design can lead to at least 28% complexity reduction.