LFSR sequences over GF(4)
I want to create sequences generated by the polynomial x2+αx+1 where coefficients are from F4 s.t. α2+α+1=0. In which α2=α+1 and α3=1.
There are 16 initial states which are:
00,01,0α,0α2
10, 11, 1α, 1α2
α0, α1, αα2, αα2
α20, α21, α2α, α2α2
For example, by starting with initial state αα2, we get 1α + αα2= α+α3= α+1= α2.
Now the sequence is αα2α2. To find the 4. item we will use the new state α2α2 and we get 1α2 + αα2= α2+α3= α2+1= α.
Now the sequence is αα2α2α.
By the same way we get the sequence αα2α2α0αα2α2... of period 5. I could not write the sage code to create the sequence.
Is this a homework?
No. I am studying sequences over extension fields. I need make with a program. I tryed to make on SAGE but I could not. If I can define a recurring sequence over GF(4) then I can apply to other examples.
Check out documentation and examples at https://doc.sagemath.org/html/en/refe...
I checked this document page. The elements of F=GF(4) are (0, 1, 0, 1) in order. I dont get it and asked for help here.
Please add to your question a Sage code you have trouble with, along with the expected outcome.