LFSR/PRBS

Linear feedback shift registers (LFSRs), or their software implementations, are used to generate pseudo-random binary sequences (PRBS, also referred to as pseudo-random bit sequences) which are largely used in telecommunication (data scrambling, sync and/or test patterns, field delimiter markers, jamming, stream ciphers, bit-error rate tests, ...).
The feedback is formed by XORing or XNORing the outputs of selected stages of the shift register - referred to as taps - and then inputting this to the least significant bit (stage 0). The list of the taps is known as the tap sequence. It is this feedback that causes the register to loop through repetitive sequences of pseudo-random  value.
LFSRs are described by their characteristic polynomial: for example a tap sequence of [4, 3, 0] (the 0 corresponds to the x0 = 1 and can be omitted) describes the  polynomial x^4+x^3+1 (a 4-bit shift-register):

Last update:  22th December, 2020

Below a table of the polynomials  you may find in this blog is shown along with the systems where they are employed; the LFSR polynomials used in STANAG, MIL-STD, and FED standards are not listed.

 polynomial referring post (used as) x^31+x^3+1 KW-46 encryption (sync) x^11+x^9+1 CIS 81-81 T-206 (scrambler?) x^9+x^5+1 100-50Bd/500 FSK-2 (sync/test pattern) CIS-12 (T-230) (sync/test pattern) 318KBd/228 GFSK (scrambler) x^8+x^6+x+1 SAAB GRINTEG MHF 50 CIS-75 (128-bit) x^7+x^6+1 CIS-75 126-bit (sync/test pattern, one bit in error) French-Ny 50Bd/850 FSK-2 (marker) x^7+x^5+x+1 50Bd/500 FSK-2 x^7+x^3+1 Swiss Army TC-535 (PN sequence generator) x^6+x^5+1 French-Ny 50Bd/850 FSK-2 (marker) 300Bd/500 FSK-2 (scrambler?) STANAG-4481F (test pattern?) x^5+x^4+x+1 50Bd/500 FSK-2 200Bd/400 MFSK-4 x^5+x^4+1 CIS-11 idle signal β x^4+x^3+1 CIS-Ny "Akula" (scrambler) x^3+x^2+x+1 256-bit Initialization Vectors encryption system x^3+x^2+1 CIS-11 idle signal α (used as sync/test in d0-d4,s0-s1 bits)