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Generation of canonical M-sequences and dual bases

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2 Author(s)
J. J. Komo ; Dept. of Electr. & Comput. Eng., Clemson Univ., SC, USA ; W. J. Reid

An expression for the shift necessary to obtain a canonical M-sequence is obtained in terms of the coefficients of the primitive polynomial that generates this m-sequence. This shift for obtaining a canonical M-sequence is also directly related to the shift for obtaining the location of the span “100...0” in the M-sequence. In addition, a recursion is developed for obtaining the dual basis elements of the basis expressing GF(qm) over GF(q). Canonical M-sequences and dual bases are important in the design of sequences for spread-spectrum multiple-access systems as well as in the design of general decoder structures using bit-serial encoders

Published in:

IEEE Transactions on Information Theory  (Volume:42 ,  Issue: 2 )