Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a partial spread is ``big enough", then the corresponding linear code is minimal. They used the sufficient condition in (IEEE Trans. Inf. Theory 44(5): 2010-2017, 1998) to prove the minimality of such linear codes. In this paper, we use the geometric approach to study the minimality of linear codes constructed from partial spreads in all cases.

翻译：摘要：部分展形在有限几何中具有重要意义，可用于构造线性码。根据Xia Li、Qin Yue和Deng Tang在《Designs, Codes and Cryptography》90:1-15, 2022中的结果，若部分展形中元素的数量“足够大”，则相应的线性码为最小码。他们运用《IEEE Trans. Inf. Theory》44(5): 2010-2017, 1998中的充分条件证明了此类线性码的最小性。本文采用几何方法，研究所有情形下由部分展形构造的线性码的最小性。