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In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value.
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field.
It is easy to detect the structure of a linear-feedback shift register with appropriate tests [41] such as the linear complexity test implemented in the TestU01 suite; a Boolean circulant matrix initialized from consecutive bits of an LFSR will never have rank greater than the degree of the polynomial.
They are a subset of linear-feedback shift registers (LFSRs) which allow a particularly efficient implementation in software without the excessive use of sparse polynomials. [2] They generate the next number in their sequence by repeatedly taking the exclusive or of a number with a bit-shifted version of itself. This makes execution extremely ...
In fact, every linear-feedback shift register with maximum cycle length (which is 2 n − 1, where n is the length of the linear-feedback shift register) may be built from a primitive polynomial. [2] In general, for a primitive polynomial of degree m over GF(2), this process will generate 2 m − 1 pseudo-random bits before repeating the same ...
A maximum length sequence (MLS) is a type of pseudorandom binary sequence.. They are bit sequences generated using maximal linear-feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except the zero vector) that can be represented by the shift registers (i.e., for length-m registers they produce a sequence of length 2 m − 1).
This example will use the connection polynomial x 8 + x 4 + x 3 + x 2 + 1, and an initial register fill of 1 0 1 1 0 1 1 0. Below table lists, for each iteration of the LFSR, its intermediate output before self-shrinking, as well as the final generator output. The tap positions defined by the connection polynomial are marked with blue headings.
Furthermore, the algorithm used to verify the polynomials is not state of the art. I.e., one common algorithm used to test if a LFSR has maximal length is to first check if the feedback polynomial is irreducible, i.e. by trying to factor the polynomial.
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