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Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉
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 Z4 arising from the chain ring Z4[u]/u2+1. Our construction produces self-orthogonal codes over Z4 with increased lengths and free ranks from given self-orthogonal codes over Z4 with smaller lengths and free ranks; in the most of the cases their minimum weights are also increased. Furthermore, any self-orthogonal code over Z4 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 Z4 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 Z4 with the same type. As a method, we use additive codes over the finite ring Z4[u]/u2+1 with generator matrices G satisfying GGT=O, and we use a new Gray map from Z4[u]/u2+1 to Z43 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 Z4 由链环引起 Z4[]/2+1. 我们的结构产生自正交代码Z4 从给定的自正交代码增加长度和自由等级 Z4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Z4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Z4至等价;其中,距离最优的自正交码有35。此外,我们有八个自正交码,它们是所有线性码中距离最优Z4相同类型的。作为一种方法,我们在有限环上使用加法代码Z4[]/2+1生成矩阵G满足GG=,我们使用来自 Z4[]/2+1Z43 以及。

更新日期:2021-12-30
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