Abstract: The paper provides an in-depth tutorial of mathematical
construction of maximal length sequences (m-sequences) via primitive
polynomials and how to map the same when implemented in
shift registers. It is equally important to check whether a polynomial
is primitive or not so as to get proper m-sequences. A fast method to
identify primitive polynomials over binary fields is proposed where
the complexity is considerably less in comparison with the standard
procedures for the same purpose.