In this paper, we construct several infinite families of $q$-ary constacyclic codes over a finite field $\mathbb{F}_q$ with length $n$, dimension around $n/2$, and minimum distance at least $cn/\log_q n$ for some positive constant $c$. They contain many constacyclic codes with optimal, or almost-optimal, or best-known parameters. We also consider constacyclic codes of various lengths.

翻译：在本文中，我们构造了有限域 $\mathbb{F}_q$ 上若干无穷族 $q$ 元常循环码，其长度为 $n$，维数约为 $n/2$，且对于某个正常数 $c$，最小距离至少为 $cn/\log_q n$。这些码包含了许多参数为最优、接近最优或具有最佳已知参数的常循环码。我们还考虑了不同长度的常循环码。