I'm an Electronics Engineer with a love for math so due to my background pardon me if my description is inadequate (I tried hard to make it formally correct).
Context and motivation:
I have been working with Sidel'nikov sequences and through exploratory analysis I found that some sequences are contained in lengthier ones.
Consider only binary sequences and for a Fermat prime.
Although not the original definition, the positions of "1" in a Sidel'nikov sequence can be determined using the Zech log,
or alternatively with a primitive element of and . To be entirely correct belongs to a prime residue group, so but since we are restricting ourselves to Fermat primes then we can just consider to be in the set of all the odd integers less than .
A numerical example using Mathematica:
For a sequence of length 16 with primitive element 3,