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In this paper, it is shown how to synthesize simple decoders for cyclic product codes. Cyclic product codes may be synthesized in the form of interlaced codes if the block lengths of the codes are relatively prime. In this case, the decoder can be synthesized in the form of a cascade of decoders, each of which operates on one of the subcodes forming the product code. The cascade decoders described differ from most of the decoders given in the coding literature in two major respects. First, they can be built. Second, instead of correcting all error patterns with weight less than some fixed value and no error patterns of greater weight, cascade decoders correct many error patterns beyond their guaranteed correction capability. Thus, the effective error-correction performance using a cascade decoder may be considerably beyond the usual Elias bound for product codes.