论文标题
MACAULAY的编码理论软件包2
Coding theory package for Macaulay2
论文作者
论文摘要
在此macaulay2 \ cite {m2}包中，我们定义了一个称为{\ it linear code}的对象。我们实现了计算与线性代码相关的基本参数和对象的功能，例如生成器和奇偶校验检查矩阵，双代码，长度，维度和最小距离等。我们定义一个对象{\ it评估代码}，该构建允许使用代数几何和交换代数的工具来研究线性代码。我们实施功能来生成重要的线性代码族，例如锤码代码，循环代码，芦苇 - 固体代码，芦苇代码 - 毛茸茸的代码，笛卡尔代码，单一代码 - - 卡特斯码 - - 卡特斯码和摩托图形代码。此外，我们定义了综合征解码算法和局部可回收代码构建的功能，这是线性代码应用中的重要工具。 \ url {https://github.com/macaulay2/workshop-2020-cleveland/tree/codingtheory/codingore}
In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code, length, dimension, and minimum distance, among others. We define an object {\it evaluation code}, a construction which allows to study linear codes using tools of algebraic geometry and commutative algebra. We implement functions to generate important families of linear codes such as Hamming codes, cyclic codes, Reed--Solomon codes, Reed--Muller codes, Cartesian codes, monomial--Cartesian codes, and toric codes. In addition, we define functions for the syndrome decoding algorithm and locally recoverable code construction, which are important tools in applications of linear codes. The package \textit{CodingTheory.m2} is available at \url{https://github.com/Macaulay2/Workshop-2020-Cleveland/tree/CodingTheory/CodingTheory}
