J. Y. Hyun, et al. (Des. Codes Cryptogr., vol. 88, pp. 2475-2492, 2020) constructed some optimal and minimal binary linear codes generated by one or two order ideals in hierarchical posets of two levels. At the end of their paper, they left an open problem: it also should be interesting to investigate the cases of more than two orders in hierarchical posets with two levels or many levels. In this paper, we use the geometric method to determine the minimality of linear codes generated by any orders in hierarchical posets with two levels. We generalize their cases of one or two orders to any orders and determine the minimality of the linear codes completely.

翻译：J. Y. Hyun 等人（《设计与编码密码学》，第88卷，第2475-2492页，2020年）通过两级分层偏序集中一个或两个序理想构造出若干最优且最小的二元线性码。该文末尾提出一个开放问题：研究两级或多级分层偏序集中超过两个序的情形同样具有意义。本文采用几何方法，判定两级分层偏序集中任意序所生成线性码的最小性，将上述一个或两个序的情形推广至任意序，并完整确定了这些线性码的最小性条件。