Answered: Question 7. Let g(X) = X¹ + X³ + X² + 1…

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Question 7. Let g(X) = X¹ + X³ + X² + 1 € F₂[X]. We consider a [7, 3]- cyclic code C of generator g(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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For this question I have to find a parity check polynomial of C and determine whether [1,1,1,0,0,1,0]. For the parity check polynomial I got x^3-1 which I'm not sure if it's correct? And how do I check whether [1,1,1,0,0,1,0] is in C or not?

Question 7. Let g(X) = X¹ + X³ + X² + 1 € F₂[X]. We consider a [7, 3]-
cyclic code C of generator g(X).

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Step 1: Check the parity of the polynomial

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Step 2: Check whether [1,1,1,0,0,1,0] is in C or not

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