Generation of canonical M-sequences and dual bases

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(q^m) 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