Question

LFSR (a) What is a primitive polynomial P(x) in the context of LFSRs? (b) Compute the...

LFSR

(a) What is a primitive polynomial P(x) in the context of LFSRs?

(b) Compute the sequence of states of the LFSRs defined by polynomial P(x) = x 3+x 2+1. Initialize the state with the binary string 110. Is P(x) primitive?

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Answer #1

(a) LFSR(Linear Feedback Shift Register)

In LFSR, a primitive polynomial is a characteristic polynomial which generates a maximum length sequence.

A maximum length sequence is pseudo-random.

(b)

Yes. The given function is a primitive function.

Number of states can be calculated by formula , where n is the higher order degree. Here 3.

Therefore number of states here is which is 7.

Sequence of states can be listed as

1 1 0

0 1 1

1 1 1

1 0 1

1 0 0

0 1 0

0 0 1

0 0
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