论文标题
$ \ mathbb {z} _4 $代码的更新的数据库
An Updated Database of $\mathbb{Z}_4$ Codes
论文作者
论文摘要
自1994年发现以来，对有限环的代码进行的研究加剧了，即可以作为$ \ Mathbb {z} _4 $ - 线性代码获得一些最佳的二进制非线性代码。在这一发现之后，许多不同有限环上的代码一直是编码理论的大量研究主题。这些环中的许多是$ \ mathbb {z} _4 $的扩展。结果，在2008年创建了$ \ mathbb {z} _4 $的在线数据库。本文的目的是介绍$ \ mathbb {z} _4 $代码的新的更新的数据库。我们通过在$ \ mathbb {z} _4 $上添加8701个新的线性代码来对数据库进行了重大更新。通过详尽的计算机搜索循环代码和ASR搜索算法的实现，这些代码是通过详细的计算机搜索发现的，该算法的实现非常有效，可以从准循环（QC）（QC）类别中获得新的线性代码，并在有限字段上获得了QASI-CYCLIC（QC）（QC）代码（QT）代码。我们对ASR算法进行了修改，以使其通过$ \ Mathbb {Z} _4 $进行。最初的数据库包含几乎没有免费的代码。我们添加了大量非免费代码。实际上，在我们添加的8701个代码中，其中有7631个是非免费的。
Research on codes over finite rings has intensified since the discovery in 1994 of the fact that some best binary non-linear codes can be obtained as images of $\mathbb{Z}_4$-linear codes. Codes over many different finite rings has been a subject of much research in coding theory after this discovery. Many of these rings are extensions of $\mathbb{Z}_4$. As a result, an online database of $\mathbb{Z}_4$ was created in 2008. The URL of the original database on $\mathbb{Z}_4$ codes has recently changed. The purpose of this paper is to introduce the new, updated database of $\mathbb{Z}_4$ codes. We have made major updates to the database by adding 8701 new linear codes over $\mathbb{Z}_4$. These codes have been found through exhaustive computer searches on cyclic codes and by an implementation of the ASR search algorithm that has been remarkably fruitful to obtain new linear codes from the class of quasi-cyclic (QC) and quasi-twisted (QT) codes over finite fields. We made modifications to the ASR algorithm to make it work over $\mathbb{Z}_4$. The initial database contained few codes that were not free. We have added a large number of non-free codes. In fact, of the 8701 codes we have added, 7631 of them are non-free.
