it uses CRC-16-CCITT for PHY headers). CRC-32C computation is implemented in hardware as an operation () of SSE4.2 instruction set, first introduced in Intel processors' Nehalem microarchitecture. ARM AArch64 architecture also provides hardware acceleration for both CRC-32 and CRC-32C operations. Polynomial representations of cyclic redundancy checks The table below lists only the polynomials of the various algorithms in use. Variations of a particular protocol can impose pre-inversion, post-inversion and reversed bit ordering as described above. For example, the CRC32 used in Gzip and Bzip2 use the same polynomial, but Gzip employs reversed bit ordering, while Bzip2 does not. Note that even parity polynomials in GF(2) with degree greater than 1 are never primitive. Even parity polynomial marked as primitive in this table represent a primitive polynomial multiplied by . The most significant bit of a polynomial is always 1, and is not shown in the hex representations. Implementations Implementation of CRC32 in GNU Radio up to 3.6.1 (ca. 2012) C class code for CRC checksum calculation with many different CRCs to choose from CRC catalogues Catalogue of parametrised CRC algorithms CRC Polynomial Zoo See also Mathematics of cyclic redundancy checks Computation of cyclic redundancy checks List of hash functions List of checksum algorithms Information security Simple file verification LRC References Further reading External links Cyclic Redundancy Checks, MathPages, overview of error-detection of different polynomials Algorithm 4 was used in Linux and Bzip2. , Slicing-by-4 and slicing-by-8 algorithms — Bitfilters — theory, practice, hardware, and software with emphasis on CRC-32. Reverse-Engineering a CRC Algorithm — includes links to PDFs giving 16 and 32-bit CRC Hamming distances ISO/IEC 13239:2002: Information technology -- Telecommunications and information exchange between systems -- High-level data link control (HDLC) procedures CRC32-Castagnoli Linux Library Binary arithmetic Finite fields Polynomials Wikipedia articles with ASCII art Articles with example Python (programming language) code