论文标题
在Reed-Muller和Simplex代码中保存的T-Designs的线性代码
The linear codes of t-designs held in the Reed-Muller and Simplex codes
论文作者
论文摘要
Comminatorics的一个有趣的话题是$ t $ - 设计，历史悠久。 $ t $ design的发射机矩阵对任何Prime Power $ Q $生成了线性代码（Q）$，这称为GF $（Q）$的$ t $ - design的线性代码。另一方面，某些线性代码容纳$ t $ designs的某些$ t \ geq 1 $。本文的目的是研究在Reed-Muller和Simplex代码中保存的一些$ t $ designs的线性代码。提出了一些在线性代码中持有的$ t $ - 设计线性代码的一般理论。还提出了开放问题。
A fascinating topic of combinatorics is $t$-designs, which have a very long history. The incidence matrix of a $t$-design generates a linear code over GF$(q)$ for any prime power $q$, which is called the linear code of the $t$-design over GF$(q)$. On the other hand, some linear codes hold $t$-designs for some $t \geq 1$. The purpose of this paper is to study the linear codes of some $t$-designs held in the Reed-Muller and Simplex codes. Some general theory for the linear codes of $t$-designs held in linear codes is presented. Open problems are also presented.
