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LFSR sequences over GF(4)

asked 2 years ago

Kenan gravatar image

updated 2 years ago

FrédéricC gravatar image

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.

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Is this a homework?

Max Alekseyev gravatar imageMax Alekseyev ( 2 years ago )

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.

Kenan gravatar imageKenan ( 2 years ago )
1

Check out documentation and examples at https://doc.sagemath.org/html/en/refe...

Max Alekseyev gravatar imageMax Alekseyev ( 2 years ago )

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.

Kenan gravatar imageKenan ( 2 years ago )
1

Please add to your question a Sage code you have trouble with, along with the expected outcome.

Max Alekseyev gravatar imageMax Alekseyev ( 2 years ago )

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answered 2 years ago

Max Alekseyev gravatar image

updated 1 year ago

Is this what you want?

K.<a> = GF(4, modulus=[1,1,1])
L = lfsr_sequence([1,a], [0,1], 20)
print(L)
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Thanks a lot dear Max Alekseyev

Kenan gravatar imageKenan ( 1 year ago )

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Asked: 2 years ago

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Last updated: Feb 21 '23