Finite Fields and Their Applications ( IF 1 ) Pub Date : 2021-11-24 , DOI: 10.1016/j.ffa.2021.101972 Boran Kim , Nayoung Han , Yoonjin Lee
We find a building-up type construction method for self-orthogonal codes over arising from the chain ring . Our construction produces self-orthogonal codes over with increased lengths and free ranks from given self-orthogonal codes over with smaller lengths and free ranks; in the most of the cases their minimum weights are also increased. Furthermore, any self-orthogonal code over with generator matrix subject to certain conditions can be obtained from our construction. Employing our construction method, we obtain at least 125 new self-orthogonal codes over up to equivalence; among them, there are 35 self-orthogonal codes which are distance-optimal. Furthermore, we have eight self-orthogonal codes, which are distance-optimal among all linear codes over with the same type. As a method, we use additive codes over the finite ring with generator matrices G satisfying , and we use a new Gray map from to as well.
中文翻译:
由链环 Z4[u]/〈u2+1> 产生的 Z4 上的自正交码
我们找到了一种自正交码的组合式构造方法 由链环引起 . 我们的结构产生自正交代码 从给定的自正交代码增加长度和自由等级 具有较小的长度和自由行列;在大多数情况下,它们的最小权重也会增加。此外,任何自正交代码可以从我们的构造中获得受某些条件约束的生成器矩阵。使用我们的构造方法,我们获得了至少 125 个新的自正交代码至等价;其中,距离最优的自正交码有35个。此外,我们有八个自正交码,它们是所有线性码中距离最优的与相同类型的。作为一种方法,我们在有限环上使用加法代码生成矩阵G满足,我们使用来自 到 以及。