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The distribution of (n-m) terms for maximal length linear pseudo-random sequences (Corresp.)

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The number of(n - m)terms as a function of the length between their recurrence is derived for maximal length linearn-stage shift-register generated sequences. An(n - m)term is defined as that state remaining following specification ofmcomponents, of thencomponent shift-register state, as "don't care" variables. The derivation makes application of the cycle-and-add property for such sequences. The distribution is shown to be of value(2^{m} - 1)for all recurrence lengths less than the period of the sequence and of value(2^{n} - 1)when the recurrence length is equal to the period of the sequence. [1] In addition, it is concluded that the distribution of(n - m)terms for de Bruijn sequences (maximal-length nonlinear recursions) is dependent upon(n - m)term construction.

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Information Theory, IEEE Transactions on  (Volume:14 ,  Issue: 4 )