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Finite Fields and Their Applications
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Finite Fields and Their Applications
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Let 00. Define S(f,n)=@?"x"@?"F"""2"""^"""ne(f(x)) where m|n and e(x)=(-1)^T^r^"^F^"^"^"^2^"^"^"^^^"^"^"^n^"^/^"^F^"^"^"^2^(^x^). We establish a relation among S(f,n) for all n with the same 2-adic order. When @n"2(@a"1)=...=@n"2(@a"k), where @n"2 is the 2-adic order function, we are able to compute S(f,n) explicitly for all n with a given f. Moreover, we are able to compute S(ax^2^^^@a^+^1+cx,n) explicitly for all @a0, a@?F"2"^"m, m|n and c@?F"2"^"n.