In 2018, Ding et al. introduced a new generalisation of the punctured binary Reed-Muller codes to construct LCD codes and 2-designs. They studied the minimum distance of the codes and proposed an open problem about the minimum distance. In this paper, several new results on the minimum distance of the generalised punctured binary Reed- Muller are presented. Particularly, some of the results are a generalisation or improvement of previous results in (Finite Fields Appl. 53, 144–174, 2018).

中文翻译：

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删余的二进制Reed-Muller码的新概括的最小距离

2018年，丁等人。介绍了穿孔二进制Reed-Muller码的新概括，以构建LCD码和2设计。他们研究了代码的最小距离，并提出了有关最小距离的开放问题。在本文中，提出了关于广义打孔二进制Reed-Muller最小距离的一些新结果。特别地，一些结果是一个一般化或（有限域申请先前结果的改善53，144-174，2018）。