Let Z2[x] represent all finite degree polynomials with coefficients in GF(2). Construct the finite field Z2[x]/( x4+x+1 ) which is isomorphic to GF(24). Let α be a root of the primitive polynomial x4+x+1. Develop a table to show the relationship between the multiplicative and additive representation of each element of this finite field. If possible explain in detail how this is done, I am still a little lost on how this works. Thank you.

Let Z2[x] represent all finite degree polynomials with coefficients in GF(2). Construct the finite field Z2[x]/( x4+x+1 ) which is isomorphic to GF(24). Let α be a root of the primitive polynomial x4+x+1. Develop a table to show the relationship between the multiplicative and additive representation of each element of this finite field. If possible explain in detail how this is done, I am still a little lost on how this works. Thank you.

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 Z₂[x] represent all finite degree polynomials with coefficients in GF(2). Construct the finite field Z₂[x]/( x⁴+x+1 ) which is isomorphic to GF(2⁴). Let α be a root of the primitive polynomial x⁴+x+1. Develop a table to show the relationship between the multiplicative and additive representation of each element of this finite field. If possible explain in detail how this is done, I am still a little lost on how this works. Thank you.

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