论文标题
线性和小组完美的代码在偏斜字段和准偏斜字段上
Linear and group perfect codes over skew fields and quasi skew fields
论文作者
论文摘要
在本文中，我们提出了一般的线性代码在无限偏斜字段和右（左）统一的准偏斜场上的一般结构。给出了此类代码对关联偏斜字段的完整分类。由于所考虑的偏斜场的基数是无限的，因此构造的代码具有无限的长度。在以前的工作中，我们考虑了无限可数字段的代码，其长度也可计数。现在，我们删除了此限制，并考虑偏斜场的基数和代码的长度可以是任意的（不一定是可计数的）。
In this paper, we propose a general construction of linear perfect codes over infinite skew fields and quasi skew fields with right (left) unity. A complete classification of such codes over associative skew fields is given. Since the cardinality of the considered skew fields is infinite, the constructed codes have an infinite length. In the previous work, we considered codes over infinite countable fields, the length of which was also countable. We now remove this restriction and consider that the cardinality of the skew field and the length of the codes can be arbitrary (not necessarily countable).
