论文标题
在有限磁场上具有消失的痕迹和相互迹线的不可还原多项式的数量
The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace
论文作者
论文摘要
我们介绍了有限字段$ \ mathbb f_q $的一元$ n $多项式多项式数量的公式，其中$ x^{n-1} $的系数和$ x $ nish of $ n \ ge3 $。特别是，我们在\ mathbb f_ {q^n} $ in trace $（a）= 0 $ and trace $（a^{ - 1}）= 0 $之间给出了有限字段的代数曲线的理性点与元素$ a \ in y mathbb f_ {q^n} $之间的关系。此外，我们将公式应用于具有良好家庭复杂性和互相关度量的序列家族的不同构建体的上限。
We present the formula for the number of monic irreducible polynomials of degree $n$ over the finite field $\mathbb F_q$ where the coefficients of $x^{n-1}$ and $x$ vanish for $n\ge3$. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements $a\in\mathbb F_{q^n}$ for which Trace$(a)=0$ and Trace$(a^{-1})=0$. Besides, we apply the formula to give an upper bound on the number of distinct constructions of a family of sequences with good family complexity and cross-correlation measure.
