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Burst error correcting codes, such as fire codes, have traditionally been decoded using linear feedback shift registers (LFSR). However, such sequential decoding schemes are not suitable for modern ultra high-speed channels that demand high-speed parallel decoding employing only combinational logic circuitry. This work proposes a parallel decoding method for cyclic burst error correcting codes. Under this method, a binary companion matrix T defines the entire decoding process. Hence, the decoding method can be implemented using only combinational logic.