2 research outputs found
Divisibility of Weil Sums of Binomials
Consider the Weil sum , where is
a finite field of characteristic , is the canonical additive
character of , is coprime to , and . We say that
is three-valued when it assumes precisely three distinct values as
runs through : this is the minimum number of distinct values in the
nondegenerate case, and three-valued are rare and desirable. When
is three-valued, we give a lower bound on the -adic valuation of
the values. This enables us to prove the characteristic case of a 1976
conjecture of Helleseth: when and is a power of ,
we show that cannot be three-valued.Comment: 11 page