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# Cyclic redundancy check

<algorithm> (CRC or "cyclic redundancy code") A number derived from, and stored or transmitted with, a block of data in order to detect corruption.

By recalculating the CRC and comparing it to the value originally transmitted, the receiver can detect some types of transmission errors.

A CRC is more complicated than a checksum.

It is calculated using division either using shifts and exclusive ORs or table lookup (modulo 256 or 65536).

The CRC is "redundant" in that it adds no information.

A single corrupted bit in the data will result in a one bit change in the calculated CRC but multiple corrupted bits may cancel each other out.

CRCs treat blocks of input bits as coefficient-sets for polynomials.

E.g., binary 10100000 implies the polynomial: 1*x^7 + 0*x^6 + 1*x^5 + 0*x^4 + 0*x^3 + 0*x^2 + 0*x^1 + 0*x^0. This is the "message polynomial".

A second polynomial, with constant coefficients, is called the "generator polynomial". This is divided into the message polynomial, giving a quotient and remainder.

The coefficients of the remainder form the bits of the final CRC.

So, an order-33 generator polynomial is necessary to generate a 32-bit CRC.

The exact bit-set used for the generator polynomial will naturally affect the CRC that is computed.

Most CRC implementations seem to operate 8 bits at a time by building a table of 256 entries, representing all 256 possible 8-bit byte combinations, and determining the effect that each byte will have.

CRCs are then computed using an input byte to select a 16- or 32-bit value from the table.

This value is then used to update the CRC.

Ethernet packets have a 32-bit CRC.

Many disk formats include a CRC at some level.

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