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#1 2009-10-04 12:34:37

enjoymath
Guest

trace is a non-singular

How do I show that trace map defined as follows is a non-degenerate map.

tr: F_{q^n} -> F_{q}
tr(x) = sum{i=0 to n-1} x^{q^i}

I do not need full proof ... just some hints.

Thanks.

#2 2009-10-04 13:47:42

Avon
Member
Registered: 2007-06-28
Posts: 80

Re: trace is a non-singular

The trace map is a polynomial over the field F_{q^n}. How many roots can it have?

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#3 2009-10-04 14:51:42

enjoymath
Guest

Re: trace is a non-singular

Thanks. smile I did not realize it was so easy.

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