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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 7E

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Question

M4

For an irreducible polynomial p(X)=1+X +
X² e F2[X] consider F4 generated by p(X).
Find x1, x2 E F4 such that
[10] x x1 + [11] × x2 = [01]
(01] x x1 + [01] × x2 = [10].
Express r1 and x2 in vector form of length 2,
e.g., [00].

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