On the evaluation of a class of Weil sums in characteristic 2
On the evaluation of a class of Weil sums in characteristic 2
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发表时间：
1999-10
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通讯作者：
Robert S. Coulter
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作者：
Robert S. Coulter
其中χ是Fq的非平凡可加特征标，f ∈ Fq[X ].本文考虑了f（X）= aX +1 +L（X）且p = 2的所有Weil和的计算.这里，a ∈ Fq，α是任何自然数，L ∈ Fq[X ]是任何加法多项式（这意味着对于所有x，y ∈ Fq，L（x+y）= L（x）+L（y））。文[4]的一个结果将问题简化为正则可加特征标χ = χ1，且L（X）= bX，其中B ∈ Fq.因此，本文的目的是明确确定和的值
, where χ is a non-trivial additive character of Fq and f ∈ Fq[X ]. In this article we consider the evaluation of all Weil sums where f(X) = aX +1 +L(X) and p = 2. Here, a ∈ Fq, α is any natural number and L ∈ Fq[X ] is any additive polynomial (by which it is meant that L(x+y) = L(x)+L(y) for all x, y ∈ Fq). A result from [4] reduces the problem to the case χ = χ1, the canonical additive character, and L(X) = bX for some b ∈ Fq. Hence our objective in this paper is to explicitly determine the value of the sum