#15 p256. Let x^2 + x +1 be an element of the polynomial ring E= F2[x] and use b
ID: 2940507 • Letter: #
Question
#15 p256. Let x^2 + x +1 be an element of the polynomial ring E= F2[x] and use bar notation to denote passage to the quotient ring f2[x]/(x^2 +x +1) NOTE F2 is F subscript 2.a. Prove that E (bar) has elements 0,1, x, and x + 1. all have bars over them.
b. Write out the 4 X 4 addition table for E (bar) and deduce that the additive
group E bar is isomorphic to the Klein Group.
c. Write out the 4 X 4 Multiplication table for E bar adn prove that Ebar^x is
isomorphic to the cylic group of order 3. Deduce that Ebar is a field.
Explanation / Answer
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