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Applications are proposed for cyclic redundancy checks (CRCs) that have factorable rather than primitive generator polynomials. Suitable encoding and decoding methods are developed. Factored-generator CRCs are then compared with tandem CRCs that have an inner code and outer code. When the factors of the generator are used as the generators of the inner and outer codes, the two kinds of CRCs have much in common, although their codewords are different. The differences are such that the factored-generator CRC offers an architectural advantage over the tandem CRC, in that the factored-generator CRC enables symmetric partial decoding, which is useful in mixed-transmission-media and point-to-multipoint systems.