论文标题
通过重复循环代码的扭转度确定最小符号对和RT重量
Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes
论文作者
论文摘要
有各种指标用于研究错误校正代码。特别是，高密度数据存储系统为阅读和写作过程提供了不一致的存在。符号对指标是针对在某个通道中具有重叠符号对的输出的动机。引入了Rosenbloom-TSFASMAN（RT）度量标准，因为存在与多个平行通信通道上的传输有关的问题，而某些通道无法用于传输。在本文中，我们确定$ \ Mathfrak r = \ bbb f_ {p^m} [p^m} [u]/\ langle u^4 \ rangle $ fength $ n = p^k $的最小符号对重量和RT重量和RT重量。为了确定，我们明确介绍了所有不同类型的环状代码的第三扭转学位，超过了$ n $的$ \ mathfrak r $。
There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom-Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over $\mathfrak R=\Bbb F_{p^m}[u]/\langle u^4\rangle$ of length $n=p^k$. For the determination, we explicitly present third torsional degree for all different types of cyclic codes over $\mathfrak R$ of length $n$.
