Show x4 + x3 + x2 + x + 1 is irreducible over Z2.Let g(X) = x4 + x3 + x2 + 1 ∈ Z2[x]. We consider a cyclic code C in R(2, 7) withthe generator polynomial g(X).(a) Find the generator matrix for C using the generator polynomial.(b) Find a parity check polynomial of C, and find the parity check matrix for Cusing the parity check polynomial.’(c) Determine whether (1, 1, 1, 0, 0, 1, 0) is in C or not.(d) Is C a Hamming code?

Show x4 + x3 + x2 + x + 1 is irreducible over Z2.Let g(X) = x4 + x3 + x2 + 1 ∈ Z2[x]. We consider a cyclic code C in R(2, 7) withthe generator polynomial g(X).(a) Find the generator matrix for C using the generator polynomial.(b) Find a parity check polynomial of C, and find the parity check matrix for Cusing the parity check polynomial.’(c) Determine whether (1, 1, 1, 0, 0, 1, 0) is in C or not.(d) Is C a Hamming code?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 46E

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