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To maximise computation speed, an intermediate remainder can be calculated by first computing the CRC of the message modulo a sparse polynomial which is a multiple of the CRC polynomial. For CRC-32, the polynomial x 123 + x 111 + x 92 + x 84 + x 64 + x 46 + x 23 + 1 has the property that its terms (feedback taps) are at least 8 positions apart ...
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.
The reciprocal of a polynomial generates the same codewords, only bit reversed — that is, if all but the first bits of a codeword under the original polynomial are taken, reversed and used as a new message, the CRC of that message under the reciprocal polynomial equals the reverse of the first bits of the original codeword. But the reciprocal ...
a contention-free quadratic permutation polynomial (QPP). [26] An example of use is in the 3GPP Long Term Evolution mobile telecommunication standard. [27] In multi-carrier communication systems, interleaving across carriers may be employed to provide frequency diversity, e.g., to mitigate frequency-selective fading or narrowband interference. [28]
The handbook was originally published in 1928 by the Chemical Rubber Company (now CRC Press) as a supplement (Mathematical Tables) to the CRC Handbook of Chemistry and Physics. Beginning with the 10th edition (1956), it was published as CRC Standard Mathematical Tables and kept this title up to the 29th edition (1991).
It is not suitable for detecting maliciously introduced errors. It is characterized by specification of a generator polynomial, which is used as the divisor in a polynomial long division over a finite field, taking the input data as the dividend. The remainder becomes the result. A CRC has properties that make it well suited for detecting burst ...
Claressa Shields unanimously outpointed Danielle Perkins on Sunday night in the first undisputed heavyweight bout in women’s boxing to remain undefeated. Shields, a two-time Olympic gold ...
A polynomial code of length is cyclic if and only if its generator polynomial divides Since g ( x ) {\displaystyle g(x)} is the minimal polynomial with roots α c , … , α c + d − 2 , {\displaystyle \alpha ^{c},\ldots ,\alpha ^{c+d-2},} it suffices to check that each of α c , … , α c + d − 2 {\displaystyle \alpha ^{c},\ldots ,\alpha ...