关于 $$\mathbb {Z}_{4} 上的准扭曲码和广义准扭曲码+u\mathbb {Z}_{4}$$

Cryptography and Communications Pub Date : 2024-08-05 DOI:10.1007/s12095-024-00732-z

Ayoub Mounir, Abdelfattah Haily

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引用次数: 0

摘要

在本文中，我们的主要目标是研究环 $\mathbb {Z}_4 +u\mathbb {Z}_4 $上的、带有 $u^2=1$的 1-生成器 $(2+u)$-准扭曲（QT）码和 $(2+u)$-广义准扭曲（GQT）码的性质和特征。我们确定了 1 个生成器 $(2 + u)$-QT 和 $(2 + u)$-GQT 码的生成器和最小生成集的结构。此外，我们还为 R 上的自由 1-生成器（(2 + u)）-QT 和（(2 + u)）-GQT 码的最小距离建立了一个下限。此外，我们还给出了一些数值示例，说明了使用格雷映射构造一些最优（\mathbb {Z}_4\）-线性码的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On quasi-twisted codes and generalized quasi-twisted codes over $$\mathbb {Z}_{4} +u\mathbb {Z}_{4}$$

In this paper, our main objective is to examine the properties and characteristics of 1-generator $(2 + u)$-quasi-twisted (QT) codes and $(2 + u)$-generalized quasi-twisted (GQT) codes over the ring $\mathbb {Z}_4 +u\mathbb {Z}_4 $, with $u^2=1$. We determine the structure of the generators and minimal generating sets for both 1-generator $(2 + u)$-QT and $(2 + u)$-GQT codes. Additionally, we establish a lower bound for the minimum distance of free 1-generator $(2 + u)$-QT and $(2 + u)$-GQT codes over R. Furthermore, we present some numerical examples that illustrate the construction of some optimal $\mathbb {Z}_4$-linear codes using the Gray map.

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Cryptography and Communications

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