# Degree of M and Max Sequence Length for LFSR

For the LFSR mod 2, determine the degree of m and maximum sequence length

s_(i+3)≡ s_i+s_(i-2)+s_(i-4) mod 2


determine the degree of m and the maximum sequence length.

I can get the degree of $$m$$ easily by taking $$2^{(m -1)}$$, but I am confused about getting the degree of $$m$$. I don't even know what this is referring to here. Any help?

Let $i+3=j$ so your recurrence becomes $s(j)=s(j-3)+s(j-5)+s(j-7)~mod~2.$ The degree of the corresponding connection polynomial is $7$ and the polynomial itself is $c(x)=1+x^3+x^5+x^7.$ If the polynomial is primitive, then the period of the resulting LFSR sequence with nonzero initial state is $2^7-1=127.$ However this polynomial is not even irreducible since it is $(x+1)(x^6+x^5+x^2+x+1)$ modulo 2. Thus your sequence will not be maximum period. Depending on the initial conditions it will be generated by either $x+1$ or the degree 6 factor. The degree 6 polynomial turns out to be primitive, however.