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Unformatted text preview: F 2 [ x ] / ( x 4 + x +1) is such a ﬁeld and α = [ x ] is a primitive element. Then g ( x ) = ( xα )( xα 2 )( xα 3 )( xα 4 ). You need to simplify g ( x ) by the relation that α 4 + α + 1 = 0. (You don’t have to do simpliﬁcations in 4.1 because everyone knows how to multiply numbers and modulo them by 11. But here it is not directly known how to multiply these powers of α to get something in F 16 .) 1...
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This note was uploaded on 09/05/2011 for the course MATH 3360 taught by Professor Billera during the Spring '08 term at Cornell.
 Spring '08
 BILLERA
 Math, Algebra

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