Cameron-Liebler line classes were introduced in [5], and motivated by a question about orbits of collineation groups of $\mathrm{PG}(3,q)$. These line classes have appeared in different contexts under disguised names such as Boolean degree one functions, regular codes of covering radius one, and tight sets. In this paper we construct an infinite family of Cameron-Liebler line classes in $\mathrm{PG}(3,q)$ with new parameter $x={(q+1)}^2/3$ for all prime powers q congruent to 2 modulo 3. The examples obtained when q is an odd power of two represent the first infinite family of Cameron-Liebler line classes in $\mathrm{PG}(3,q)$, q even.

中文翻译：

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带参数的Cameron-Liebler线类 $X=\frac{{（q+\mathrm{1个}）}^{\mathrm{2个}}}{3}$

Cameron-Liebler线类在[5]中引入，其动机是关于 $\mathrm{PG}（3，q）$。这些线类以变名出现在不同的上下文中，例如布尔一阶函数，覆盖半径一的常规代码和紧集。在本文中，我们构造了一个无限的Cameron-Liebler线类族$\mathrm{PG}（3，q）$ 具有新参数 $X={（q+\mathrm{1个}）}^{\mathrm{2个}}/3$对于所有质数q等于2的模3。当q是2的奇数幂时获得的示例表示卡梅隆-利布勒线类的第一个无穷大族$\mathrm{PG}（3，q）$，q偶。