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

The number of terms as a function of the length between their recurrence is derived for maximal length linear -stage shift-register generated sequences. An term is defined as that state remaining following specification of components, of the 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 for all recurrence lengths less than the period of the sequence and of value when the recurrence length is equal to the period of the sequence. [1] In addition, it is concluded that the distribution of terms for de Bruijn sequences (maximal-length nonlinear recursions) is dependent upon term construction.