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Unformatted text preview: a prmitive element in F 16 , we have F 16 = { , 1 ,b,b 2 ,b 3 , ,b 14 } (Note there are exactly 16 elements). To nd the conjugate class, we can start with b , i.e. the conjugate class containing b is: { b,b 2 ,b 2 2 ,b 2 3 , } Yet we know b 2 4 = b 16 = b , so the conjugate class contains exactly 4 elements. We then take away the elements in this conjugate class from F 16 , and carry out the same calculation for the remaining elements, we will get the 6 conjugate classes: { } , { 1 } , { b,b 2 ,b 4 ,b 8 } , { b 3 ,b 6 ,b 12 ,b 9 } , { b 5 ,b 10 } , { b 7 ,b 11 ,b 13 ,b 14 } And each conjugate class gives you an irreducible polynomial of degree equal to the cardinality of the class, which is a factor of x 16x 1...
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 Spring '08
 BILLERA
 Math, Algebra

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