The note clarifies a gap in the proof of the minimum distance for Projective Reed-Muller Codes. The gap was identified by S.Ghorpade and R.Ludhani in a recent article. Here the original thoughts are explained and the gap closed.

翻译：本文注记澄清了射影Reed-Muller码最小距离证明中的一处缺失。该缺失由S.Ghorpade与R.Ludhani在近期的一篇文章中指出。本文对原始思路进行了阐释，并填补了该缺失。