13. Let g(x) be a polynomial in Z₂[x]. Prove that if the polynomial code C generated by g(x) with length n iscyclic, then g(x) is a factor of x" + 1 in Z₂[x].

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Answered: Let g(x) be a polynomial in Z₂[x].…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let g(x) be a polynomial in Z₂[x]. Prove that if the polynomial code C generated by g(x) with length n is cyclic, then g(x) is a factor of x + 1 in Z₂[x].