A fascinating topic of combinatorics is the study of t-designs, which has 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 with t ≥ 1. The purpose of this paper is to study the linear codes of 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. Several open problems are also presented.

中文翻译：

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Reed-Muller和Simplex代码中包含的t设计的线性代码

组合设计的一个引人入胜的话题是t设计的研究，该历史由来已久。t设计的入射矩阵针对任何素数q在GF（q）上生成一个线性码，这称为t设计在GF（q）上的线性码。在另一方面，一些线性码举行牛逼-designs与牛逼≥1.本文的目的是研究的线性码牛逼里德-穆勒和单纯码-designs举行。提出了关于线性设计中t设计的线性码的一些一般理论。还提出了几个未解决的问题。