论文标题
有限字段上的新MDS自偶代码$ \ f_ {r^2} $
New MDS self-dual codes over finite fields $\F_{r^2}$
论文作者
论文摘要
MDS自偶像代码具有不错的代数结构，并由长度唯一决定。最近，在编码理论中，新长度的MDS自动划分代码的构建已成为一个重要而热门的问题。在本文中，我们开发了现有的理论，并构建了六个新类MDS自偶代码。与我们的构造一起，相对于可能的MDS自动二倍代码，所有已知的MD自偶代码的比例通常超过57 \％。据我们所知，这是最大的已知比率。此外，还构建了一些新的MDS自动守则和MD的新家族几乎是自动偶数代码。
MDS self-dual codes have nice algebraic structures and are uniquely determined by lengths. Recently, the construction of MDS self-dual codes of new lengths has become an important and hot issue in coding theory. In this paper, we develop the existing theory and construct six new classes of MDS self-dual codes. Together with our constructions, the proportion of all known MDS self-dual codes relative to possible MDS self-dual codes generally exceed 57\%. As far as we know, this is the largest known ratio. Moreover, some new families of MDS self-orthogonal codes and MDS almost self-dual codes are also constructed.
