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Interlacing properties of shift-register sequences with generator polynomials irreducible over GF(p)-herein called elementary sequences--are analyzed. The most important elementary sequences are maximal-length sequences (m-sequences). If the periodqof an elementary sequence is not prime, the sequence can always be constructed by interlacing shorter elementary sequences of periodqᵢ, providedqᵢdividesq. It is proved that all interlaced elementary sequences are generated by one and the same irreducible polynomial. Some relationships between equal-length elementary sequences are derived, including some rather unexpected crosscorrelation properties. As an example of an application of the theory, a new time-division multiplex technique for generating high-speedm-sequences is presented.
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Surböck et al. (1978) studied this question.
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