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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 19E

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