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

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1 Author(s)

The number of (n - m) terms as a function of the length between their recurrence is derived for maximal length linear n -stage shift-register generated sequences. An (n - m) term is defined as that state remaining following specification of m components, of the n component 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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IEEE Transactions on Information Theory  (Volume:14 ,  Issue: 4 )