Linear complexities of periodic sequences obtained from sequences over Z(4) and Z(8) by one-symbol substitution
In this paper, we will show that some families of periodic sequences over Z(4) and Z(8) with period multiple of 2(r) - 1 generated by r-th degree basic primitive polynomials assorted by the root of each polynomial, and give the exact distribution of sequences for each family. We also point out such an instability as an extreme increase of their linear complexities for the periodic sequences by one-symbol substitution, i.e., from the minimum value to the maximum value, for all the substitutions except one.
linear complexity sequences over z(4) and z(8) one-symbol substitution basic irreducible (primitive) polynomial