M系列のnタップル間の位相差

概要

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When we use a high-order M-sequence for generating pseudo-random numbers, we sometimes encounter the case where the selection of the initial n-tuple affects the statistical properties of the generated numbers. For example, if we choose as the initial n-tuple such an unsuitable n-tuple as the initial n-tuple of the characteristic M-sequence or its cyclotomic phases, the resulting numbers does not become random for a while. In these cases, if we know the phase difference between an unsuitable n-tuple and the n-tuple we use, we will see whether the n-tuple is suitable for initial n-tuple or not.This paper proposes a new method to calculate the phase difference between any two n-tuples. Using this method, the authors obtained the phase difference between the initial n-tuple of the characteristic M-sequence and the n-tuple containing all 1 in case of the characteristic trinomials of the form f(x) =xn+xk+1. The authors show that the phase difference is obtained as a function of n and k in case where (1) k=1, (2) k=n-2l, (3) k=2l (l: ineger).
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