In computing, a linear feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. For a general reference on the subject of LFSRs and related sequence generators, see Klapper and Goreky's book.
The most commonly used linear function of single bits is XOR. Thus, an LFSR is most often a shift register whose input bit is driven by the exclusive-or (XOR) of some bits of the overall shift register value.
The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state. Likewise, because the register has a finite number of possible states, it must eventually enter a repeating cycle. However, an LFSR with a well-chosen feedback function can produce a sequence of bits which appears random and which has a very long cycle.
Applications of LFSRs include generating pseudo-random numbers, pseudo-noise sequences, fast digital counters, and whitening sequences. Both hardware and software implementations of LFSRs are common.
The mathematics of a cyclic redundancy check, used to provide a quick check against transmission errors, are closely related to those of an LFSR.
Read more about Linear Feedback Shift Register: Fibonacci LFSRs, Galois LFSRs, Some Polynomials For Maximal LFSRs, Output-stream Properties, Applications
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