Abstract: Maximal length sequences (m-sequences) are also
known as pseudo random sequences or pseudo noise sequences
for closely following Golomb-s popular randomness properties: (P1)
balance, (P2) run, and (P3) ideal autocorrelation. Apart from these,
there also exist certain other less known properties of such sequences
all of which are discussed in this tutorial paper. Comprehensive proofs
to each of these properties are provided towards better understanding
of such sequences. A simple test is also proposed at the end of
the paper in order to distinguish pseudo noise sequences from truly
random sequences such as Bernoulli sequences.
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.