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Classify the following polynomials as either primitive, irreducible, or composite by writing either P. I or C in the corresponding answer blank below. x + x' +1 b) x +x' +1 o) x* x? + x d) x* +x* +1

Classify the following polynomials as either primitive, irreducible, or composite by writing either P. I or C in the corresponding answer blank below. x + x' +1 b) x +x' +1 o) x* x? + x d) x* +x* +1

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Chapter 2: Problem 8 Previous Problem Problem List Note: The notation from this problem is from Understanding Cryptography by Paar and Pelzi. A LFSR with m internal state bits is said to be of maximal length if any seed state (except 0) produces an output stream which is periodic with the maximal period 2" - 1. Recall that a primitive polynomial corresponds to a maximum length LFSR. Primitive polynomials are a special case of irreducible polynomials (roughly, polynomials that do not factor). In the context of LFSRS, a polynomial is irreducible if every seed state (except zero) gives an LFSR with the same period (though the period length may not be maximal). We will call a polynomial with neither of these properties composite. Classify the following polynomials as either primitive, Irreducible, or composite by writing either P. I or C in the corresponding answer blank below. a) x* +x' +x + x! +1 b) x* +x' +1 c) xt x +: d) x* +x +1
Transcribed Image Text:Chapter 2: Problem 8 Previous Problem Problem List Note: The notation from this problem is from Understanding Cryptography by Paar and Pelzi. A LFSR with m internal state bits is said to be of maximal length if any seed state (except 0) produces an output stream which is periodic with the maximal period 2" - 1. Recall that a primitive polynomial corresponds to a maximum length LFSR. Primitive polynomials are a special case of irreducible polynomials (roughly, polynomials that do not factor). In the context of LFSRS, a polynomial is irreducible if every seed state (except zero) gives an LFSR with the same period (though the period length may not be maximal). We will call a polynomial with neither of these properties composite. Classify the following polynomials as either primitive, Irreducible, or composite by writing either P. I or C in the corresponding answer blank below. a) x* +x' +x + x! +1 b) x* +x' +1 c) xt x +: d) x* +x +1
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