论文标题
二进制LCD代码和通过简单复合物的自动代码
Binary LCD Codes and Self-orthogonal Codes via Simplicial Complexes
论文作者
论文摘要
由于某些实际应用，近年来，线性互补双重（LCD）代码和自动守则引起了广泛的关注。在本文中，我们使用简单的复合物来构建无限的二元LCD代码家族和两个无限的二进制自动代码家族。此外，我们明确确定这些代码的重量分布。我们获得了具有最小权重的二进制LCD代码，并找到了一些符合Griesmer绑定的自动代码。作为示例，我们还提供了一些（几乎）{\ it最佳}二进制自动码代码和LCD {\ it距离最佳}代码。
Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary LCD codes and two infinite families of binary self-orthogonal codes. Moreover, we explicitly determine the weight distributions of these codes. We obtain binary LCD codes which have minimum weights two or three, and we also find some self-orthogonal codes meeting the Griesmer bound. As examples, we also present some (almost) {\it optimal} binary self-orthogonal codes and LCD {\it distance optimal} codes.
