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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.
To understand the advantages, start with the slice-by-2 case. We wish to compute a CRC two bytes (16 bits) at a time, but the standard table-based approach would require an inconveniently large 65536-entry table. As mentioned in § Generating the lookup table, CRC tables have the property that table[i xor j] = table[i] xor table[j].
These inversions are extremely common but not universally performed, even in the case of the CRC-32 or CRC-16-CCITT polynomials. They are almost always included when sending variable-length messages, but often omitted when communicating fixed-length messages, as the problem of added zero bits is less likely to arise.
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 ...
CRC: Cyclic redundancy check Link and other layers 24 References here. CRC-16-CCITT: Cyclic redundancy check (X.25, HDLC) Link layers Reference on CRC page. CRT: Cathode Ray Tube Television set, Computer Monitor Cathode ray tube: CSMA/CA: Carrier sense multiple access / collision avoidance Wireless IEEE Std 802.11 Downloads: CSMA/CD
CRC Handbook of Chemistry and Physics, a science reference handbook published by CRC Press CRC Standard Mathematical Tables , a mathematics reference handbook published by CRC Press Cyclic redundancy check , a type of hash function used to produce a checksum in order to detect errors in data storage or transmission
There are two fundamental limitations on when it is possible to construct a lookup table for a required operation. One is the amount of memory that is available: one cannot construct a lookup table larger than the space available for the table, although it is possible to construct disk-based lookup tables at the expense of lookup time.
The frame check sequence (FCS) is a 16-bit CRC-CCITT or a 32-bit CRC-32 computed over the Address, Control, and Information fields. It provides a means by which the receiver can detect errors that may have been induced during the transmission of the frame, such as lost bits, flipped bits, and extraneous bits.