Shift-Register Generators

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Shift-Register Generators

Compound generator of equation of above type, with m = 2, i.e generation of bits, known as shift-register, or Tauseworth, generator. We can write these bits as

b $_{i}$ = ( $a_{1}b_{i-1}+a_{2}b_{i-2}+...+a_{p-1}b_{i-p+1}+b_{i-p})$ mod 2

Subsections

where p indicates the earliest previous bit included in the sequence (a $_{p}=1)\protect$ , and the first p bits are provided; the constant c has been set equal to zero. There is a maximum of 2 $^{p}-1\protect$ distinct possible iterations before sequence repeats itself.Interesting is the existence of sequences with only two non-zero coefficients, i.e. b $_{i}$ is of the form
where bs are only single bits, $\oplus \protect$ denotes the `exclusive or' operation.

Amaury LATAILLADE 2002-11-04