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Interlacing properties of shift-register sequences with generator polynomials irreducible over GF(p) (Corresp.)

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2 Author(s)

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 periodq_{i}, providedq_{i}dividesq. 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:24 ,  Issue: 3 )

Date of Publication:

May 1978

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