论文标题
用于Hurwitz Integers代码的代数建设技术
An Algebraic Construction Technique for Codes over Hurwitz Integers
论文作者
论文摘要
令α为主要的Hurwitz整数。 Hα是Hurwitz Integer的环中相关模量功能的一组残差类别，是H的一个子集，它是所有Hurwitz Integers的集合。我们考虑左侧模块α，这项研究中相关模量函数的结构域是Zn（α），它是具有N（α）元素的普通整数的残留类环，这是Prime HurwitzIntegerα的标准。在这项研究中，我们提出了一种代数构造技术，该技术是根据两个模型操作形成的模量函数，该函数针对Hurwitz Integers上的代码。因此，我们获得了N（α）大小的Hurwitz整数的残留类环。此外，我们为两个模量函数中使用的数学符号提供了一些结果，并根据两个模量函数形成的代数构造技术。此外，我们介绍了通过图布局方法获得的图形，例如弹簧，高维和螺旋嵌入，对于相对于Hurwitz整数环中相关模量功能获得的残留类别的集合。
Let α be a prime Hurwitz integer. Hα, which is the set of residual class with respect to related modulo function in the rings of Hurwitz integers, is a subset of H, which is the set of all Hurwitz integers. We consider left congruent module α and, the domain of related modulo function in this study is ZN(α), which is residual class ring of ordinary integers with N(α) elements, which is the norm of prime Hurwitz integer α. In this study, we present an algebraic construction technique, which is a modulo function formed depending on two modulo operations, for codes over Hurwitz integers. Thereby, we obtain the residue class rings of Hurwitz integers with N(α) size. In addition, we present some results for mathematical notations used in two modulo functions, and for the algebraic construction technique formed depending upon two modulo functions. Moreover, we present graphs obtained by graph layout methods, such as spring, high-dimensional, and spiral embedding, for the set of the residual class obtained with respect to the related modulo function in the rings of Hurwitz integers.
