论文标题
关于有限字段的添加字符的注释
A note on additive characters of finite fields
论文作者
论文摘要
令$ \ mathbb f_q $为带有$ q $元素的有限字段，其中$ q $是主要功率，对于每个整数$ n \ ge 1 $，令$ \ mathbb f_ {q^n} $是唯一的$ n $ -n $ -degree Extension of $ n $ -degree扩展。 $ \ mathbb f_ {q^n} $中元素的$ \ mathbb f_q $ - 和$ \ mathbb f_ {q^n} $上的加法字符已在有限字段的存在结果证明中广泛使用（例如，原始的正常基础理论）。在本说明中，我们提供了这两个对象之间的有趣关系。
Let $\mathbb F_q$ be the finite field with $q$ elements, where $q$ is a prime power and, for each integer $n\ge 1$, let $\mathbb F_{q^n}$ be the unique $n$-degree extension of $\mathbb F_q$. The $\mathbb F_q$-orders of an element in $\mathbb F_{q^n}$ and an additive character over $\mathbb F_{q^n}$ have been extensively used in the proof of existence results over finite fields (e.g., the Primitive Normal Basis Theorem). In this note we provide an interesting relation between these two objects.
