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?
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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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) with
the 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 C
using 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?
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