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This is a practical example for the CRC-32 variant of CRC. [5] An alternate source is the W3C webpage on PNG, which includes an appendix with a short and simple table-driven implementation in C of CRC-32. [4]
The CRC and associated polynomial typically have a name of the form CRC-n-XXX as in the table below. The simplest error-detection system, the parity bit, is in fact a 1-bit CRC: it uses the generator polynomial x + 1 (two terms), [5] and has the name CRC-1.
All the well-known CRC generator polynomials of degree have two common hexadecimal representations. In both cases, the coefficient of x n {\displaystyle x^{n}} is omitted and understood to be 1. The msbit-first representation is a hexadecimal number with n {\displaystyle n} bits, the least significant bit of which is always 1.
XOR/table Paul Hsieh's SuperFastHash [1] 32 bits Buzhash: variable XOR/table Fowler–Noll–Vo hash function (FNV Hash) 32, 64, 128, 256, 512, or 1024 bits xor/product or product/XOR Jenkins hash function: 32 or 64 bits XOR/addition Bernstein's hash djb2 [2] 32 or 64 bits shift/add or mult/add or shift/add/xor or mult/xor PJW hash / Elf Hash ...
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In this respect, the Fletcher checksum is not different from other checksum and CRC algorithms and needs no special explanation. An ordering problem that is easy to envision occurs when the data word is transferred byte-by-byte between a big-endian system and a little-endian system and the Fletcher-32 checksum is computed.
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]
Since the generator polynomial is of degree 10, this code has 5 data bits and 10 checksum bits. It is also denoted as: (15, 5) BCH code. (This particular generator polynomial has a real-world application, in the "format information" of the QR code.) The BCH code with = and higher has the generator polynomial