ASR搜索算法在2-生成元准扭码中的推广
A Generalization of the ASR Search Algorithm to 2-Generator Quasi-Twisted Codes
摘要：
编码理论的主要目标之一是构造具有最佳参数和性能的编码。一类特殊的码称为准扭曲（QT）码是众所周知的，以产生良好的参数的代码。QT码的大部分工作都是在1-生成器的情况下进行的。在这项工作中，我们专注于2-生成器QT码和推广的ASR算法，已经非常有效地产生新的线性码从1-生成器QT码。此外，我们还推广了最近的一个算法来测试的循环码的等价性常循环码。该算法使得ASR搜索更加有效。作为实现我们的算法的结果，我们已经找到了103个QT码是新的类QT码。此外，这些代码中的大多数具有以下附加属性：a）它们具有与最知名的线性代码相同的参数，以及b）许多具有附加的期望属性，例如LCD和双包含。此外，我们还发现了一个二进制2-生成元QT码，这是新的（破纪录的）在所有的二进制线性码和它的扩展产生另一个破纪录的二进制线性码。
英文摘要：
One of the main goals of coding theory is to construct codes with best possible parameters and properties. A special class of codes called quasi-twisted (QT) codes is well-known to produce codes with good parameters. Most of the work on QT codes has been over the 1-generator case. In this work, we focus on 2-generator QT codes and generalize the ASR algorithm that has been very effective to produce new linear codes from 1-generator QT codes. Moreover, we also generalize a recent algorithm to test equivalence of cyclic codes to constacyclic codes. This algorithm makes the ASR search even more effective. As a result of implementing our algorithm, we have found 103 QT codes that are new among the class of QT codes. Additionally, most of these codes possess the following additional properties: a) they have the same parameters as best known linear codes, and b) many of the have additional desired properties such as being LCD and dual-containing. Further, we have also found a binary 2-generator QT code that is new (record breaking) among all binary linear codes and its extension yields another record breaking binary linear code.
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