The objectives of this paper are to survey and extend results on several classes of asymptotically good quasi-twisted codes over finite field with a low index, namely double circulant codes, double negacirculant codes, four circulant codes and four negacirculant codes. For a given length, we summarize the enumerations of the self-dual and LCD codes and supplement some expansion results. The existence of asymptotically good quasi-twisted codes relies on factorizations of special binomials over finite fields; the existence of these factorizations, in turn, with the assumption of Artin primitive root conjecture, or in some cases can be derived unconditionally by using Dickson polynomials.

本文的目的是调查和扩展几类低指数有限域上渐近良好的准扭曲码的结果，即双循环码、双反循环码、四循环码和四反循环码。对于给定的长度，我们总结了自双码和LCD码的枚举，并补充了一些扩展结果。渐近好拟扭曲码的存在依赖于有限域上特殊二项式的因式分解；这些因式分解的存在，反过来，在 Artin 原根猜想的假设下，或者在某些情况下可以通过使用 Dickson 多项式无条件地推导出来。