论文标题
Roos绑定在锤子和等级度量的偏斜循环代码
Roos bound for skew cyclic codes in Hamming and rank metric
论文作者
论文摘要
在本文中，提供了一个像Roos在一般场上偏斜循环代码的最小距离上的bune。结果符合锤式指标和等级度量。证明涉及偏斜多项式的算术特性以及对奇偶校验检查矩阵等级的分析。对于等级度量案例，还提供了一种使用偏压ROOS结合的算术算法构建规定的最低等级距离的方法。此外，使用偏斜的Roos绑定，建立了有限字段的MDS代码和MRD代码的一些示例。
In this paper, a Roos like bound on the minimum distance for skew cyclic codes over a general field is provided. The result holds in the Hamming metric and in the rank metric. The proofs involve arithmetic properties of skew polynomials and an analysis of the rank of parity-check matrices. For the rank metric case, a way to arithmetically construct codes with a prescribed minimum rank distance, using the skew Roos bound, is also given. Moreover, some examples of MDS codes and MRD codes over finite fields are built, using the skew Roos bound.
