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Cyclic redundancy check
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<p>A cyclic redundancy check (CRC) is an <a href="/facts/Error_correcting_code/cLUTUJrA">error-detecting code</a> commonly used in digital <a href="/facts/Telecommunications_network/NFCX0STS">networks</a> and storage devices to detect accidental changes to digital data. Blocks of data entering these systems get a short <i>check value</i> attached, based on the remainder of a <a href="/facts/Polynomial_long_division/MgJlJ2G7">polynomial division</a> of their contents. On retrieval, the calculation is repeated and, in the event the check values do not match, corrective action can be taken against data corruption. CRCs can be used for <a href="/facts/Error_detection_and_correction/o2rH8e3n">error correction</a> (see <a href="/facts/Mathematics_of_cyclic_redundancy_checks/8BfbcLBQ">bitfilters</a>). </p><p>CRCs are so called because the <i>check</i> (data verification) value is a <i>redundancy</i> (it expands the message without adding <a href="/facts/Entropy_(information_theory)/NLg4NLvt">information</a>) and the <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> is based on <a href="/facts/Cyclic_code/LmhezpnR"><i>cyclic</i> codes</a>. CRCs are popular because they are simple to implement in binary <a href="/facts/Computer_hardware/8jSjsCNv">hardware</a>, easy to analyze mathematically, and particularly good at detecting common errors caused by <a href="/facts/Noise_(electronics)/Izbv38Rr">noise</a> in transmission channels. Because the check value has a fixed length, the <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> that generates it is occasionally used as a <a href="/facts/Hash_function/rk6MlCt3">hash function</a>. </p>