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Function CRC32 Input: data: Bytes // Array of bytes Output: crc32: UInt32 // 32-bit unsigned CRC-32 value // Initialize CRC-32 to starting value crc32 ← 0xFFFFFFFF for each byte in data do nLookupIndex ← (crc32 xor byte) and 0xFF crc32 ← (crc32 shr 8) xor CRCTable[nLookupIndex] // CRCTable is an array of 256 32-bit constants
A CRC is called an n-bit CRC when its check value is n-bits. For a given n , multiple CRCs are possible, each with a different polynomial. Such a polynomial has highest degree n , and hence n + 1 terms (the polynomial has a length of n + 1 ).
Because a CRC is based on division, no polynomial can detect errors consisting of a string of zeroes prepended to the data, or of missing leading zeroes. However, see § Variations . All single bit errors will be detected by any polynomial with at least two terms with non-zero coefficients.
By far the most popular FCS algorithm is a cyclic redundancy check (CRC), used in Ethernet and other IEEE 802 protocols with 32 bits, in X.25 with 16 or 32 bits, in HDLC with 16 or 32 bits, in Frame Relay with 16 bits, [3] in Point-to-Point Protocol (PPP) with 16 or 32 bits, and in other data link layer protocols.
Latin square based code for non-white noise (prevalent for example in broadband over powerlines) Lexicographic code; Linear Network Coding, a type of erasure correcting code across networks instead of point-to-point links; Long code; Low-density parity-check code, also known as Gallager code, as the archetype for sparse graph codes
cksum is a command in Unix and Unix-like operating systems that generates a checksum value for a file or stream of data. The cksum command reads each file given in its arguments, or standard input if no arguments are provided, and outputs the file's 32-bit cyclic redundancy check (CRC) checksum and byte count. [1]
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[1]: section 3.2.9 An alternative is to calculate a CRC using the right shifting CRC-32 (polynomial = 0xEDB88320, initial CRC = 0xFFFFFFFF, CRC is post complemented, verify value = 0x2144DF1C), which will result in a CRC that is a bit reversal of the FCS, and transmit both data and the CRC least significant bit first, resulting in identical ...