Let \({\mathcal{R}}\) be the finite chain ring \({\mathcal{R}}={\mathbb{F}}_{p^{m}}+ u{\mathbb{F}}_{p^{m}}(u^{2} = 0)\), where p is an odd prime number and m is a positive integer. For \(\eta \in {\mathbb{F}}_{p^{m}}^{*}\), the Hamming distances of all \(\eta\)-constacyclic codes of length \(2p^{s}\) over \({\mathcal{R}}\) had already been studied in Dinh et al. (in AAECC, 2020. https://doi.org/10.1007/s00200-020-00432-0). However, such a study is incomplete. In this paper, we provide corrections to some results that appeared in Dinh et al. (2020) and we completely solve the problem of determination of the Hamming distance of \(\eta\)-constacyclic codes of length \(2p^{s}\) over \({\mathcal{R}}\).

令\（{\ mathcal {R}} \）为有限链环\（{\ mathcal {R}} = {\ mathbb {F}} _ {p ^ {m}} + u {\ mathbb {F} } _ {p ^ {m}}（u ^ {2} = 0）\），其中p是奇数质数，m是正整数。对于\（\ eta \ in {\ mathbb {F}} _ {p ^ {m}} ^ {*} \）中，所有\（\ eta \）-恒定长度为\（2p ^ { Dinh等人已经研究了\（{\ mathcal {R}} \）上的s} \）。（在AAECC中，2020年。https：//doi.org/10.1007/s00200-020-00432-0）。但是，这样的研究是不完整的。在本文中，我们对Dinh等人中出现的一些结果进行了更正。（2020），我们完全解决了确定汉明距离的问题。\（\ eta \）-在\（{\ mathcal {R}} \）上长度为\（2p ^ {s} \）的常量代码。