Derivation of the feedback taps of an LFSR from a sequence fragment

It is demonstrated that the coefficients of the feedback function and the characteristic polynomial of a linear feedback shift register can be deduced from the knowledge of the n digits following the pattern of n-1 zeros in one of the nonzero sequences of the device. This may be performed explicitly or successively by a simplified computation. It is also shown that this is equivalent to deriving the reciprocal of the impulse response of the equivalent sequential filter.