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Mathematics of cyclic redundancy checks

The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF(2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around.

Formulation, Error detection strength & Variations

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Overview

Formulation

Polynomial arithmetic modulo 2

Variations

Reversed representations and reciprocal polynomials

Error detection strength

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Mathematics of cyclic redundancy checks

Nodes41
Edges40
Triples2
Avg. degree1.95
Density0.04878
Components1

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Important terminology

displaystyle polynomial crc message generator bit polynomials zero bits errors remainder degree division coefficients cdot coefficient used detected modulo non-zero

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
endiannessinstance ofImplementation variations0.80text
CRC presentation only affect the mapping of bit strings to the coefficients of Minstance ofImplementation variations0.80text

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