准扭码的一种推广：多扭码
A Generalization of Quasi-twisted Codes: Multi-twisted codes
摘要：
循环码及其各种推广，如准扭曲（QT）码，在代数编码理论中有特殊的地位。除此之外，许多最著名的或最佳的代码已经从这些类中获得。在这项工作中，我们介绍了一个新的推广QT码，我们称之为多扭（MT）码，并研究了它们的一些基本性质。提出了几种方法，在这个类中的代码，并获得最小距离的界限，我们表明，存在代码，在这个类中的好参数，不能得到QT或常循环码。这表明，在计算机搜索中考虑这一较大的类是有希望的，以更好的参数比目前最知名的线性码构造代码。工作与这一类新的代码促使我们考虑一个问题的二项式在有限领域，并发现一个结果，这是有趣的本身。
英文摘要：
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this work we introduce a new generalization of QT codes that we call multi-twisted (MT) codes and study some of their basic properties. Presenting several methods of constructing codes in this class and obtaining bounds on the minimum distances, we show that there exist codes with good parameters in this class that cannot be obtained as QT or constacyclic codes. This suggests that considering this larger class in computer searches is promising for constructing codes with better parameters than currently best-known linear codes. Working with this new class of codes motivated us to consider a problem about binomials over finite fields and to discover a result that is interesting in its own right.
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