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Let Fg elements be represented with the binary polynomials where p(x)=x²+x+1=0 mod 2 and x-x=0 mod 2. 0 Find the powers 1 2² x² +1 x + x for k=1, 2, 3,..., 8 in terms of the field elements ax²+bx+c. x x+1 x²+x+1

Let Fg elements be represented with the binary polynomials where p(x)=x²+x+1=0 mod 2 and x-x=0 mod 2. 0 Find the powers 1 2² x² +1 x + x for k=1, 2, 3,..., 8 in terms of the field elements ax²+bx+c. x x+1 x²+x+1

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.6: Algebraic Extensions Of A Field
Problem 14E
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Let Fg elements be represented with the binary polynomials where p(x)=x²+x+1=0 mod 2 and x8-x=0 mod 2. 0 1 x + 1 1² x²+1 x² + x Find the powers for k=1,2,3,..., 8 in terms of the field elements ax²+bx+c. x x²+x+1
Transcribed Image Text:Let Fg elements be represented with the binary polynomials where p(x)=x²+x+1=0 mod 2 and x8-x=0 mod 2. 0 1 x + 1 1² x²+1 x² + x Find the powers for k=1,2,3,..., 8 in terms of the field elements ax²+bx+c. x x²+x+1
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