Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems related to cyclic codes. In this work, we use recent results on the equivalence of cyclic codes to create a more efficient algorithm to partition cyclic codes by equivalence based on cyclotomic cosets. This algorithm is then implemented to carry out computer searches for both cyclic codes and quasi-cyclic (QC) codes with good parameters. We also generalize these results to repeated-root cases. We have found several new linear codes that are cyclic or QC as an application of the new approach, as well as more desirable constructions for linear codes with best known parameters. With the additional new codes obtained through standard constructions, we have found a total of 14 new linear codes.

出于理论和实践的原因，循环码是编码理论中最重要的码族之一。尽管半个多世纪以来他们对循环码进行了突出和深入的研究，但仍然存在与循环码相关的开放问题。在这项工作中，我们使用最近关于循环码等价的结果来创建一种更有效的算法，以基于循环陪集通过等价划分循环码。然后实施该算法以对具有良好参数的循环码和准循环 (QC) 码进行计算机搜索。我们还将这些结果推广到重复根情况。我们已经发现了几种新的循环或 QC 线性码作为新方法的应用，以及更理想的线性码结构，其具有最广为人知的参数。