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On the Construction of m-Sequences via Primitive Polynomials with a Fast Identification Method

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. Keywords—Finite field, irreducible polynomial, primitive polynomial, maximal length sequence, additive shift register, multiplicative shift register.