Dekodowanie kodów cyklicznych

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Decoding cyclic codes Following the Conclusion to check whether the received sequence is a code word of an cyclic code, is divided by , a reminder is designated. This reminder can be considered as syndrome polynomial of ,
and it determines a decoder decision, following the strategy of (5.2.25) for error detecting decoding or (5.2.26) for error correcting decoding. For a cyclic code, relationship between a codeword, error pattern and the received sequence (5.1.1), in polynomial notation (indexes have been omitted):
Then, from (7.1.22) and (7.1.20): and taking into account As can be seen, for each error polynomial , the corresponding syndrome polynomial can be designated. Thus, for an cyclic code, error-syndrome look-up table can be constructed and used to error correction. The decoder decision (5.2.26), in polynomial notation:
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