Twisted generalized Reed-Solomon (TGRS) codes, as a flexible extension of classical generalized Reed-Solomon (GRS) codes, have attracted significant attention in recent years. In this paper, we construct two classes of LCD codes from the $(\mathcal{L},\mathcal{P})$-TGRS code $\mathcal{C}_h$ of length $n$ and dimension $k$, where $\mathcal{L}=\{0,1,\ldots,l\}$ for $l\leq n-k-1$ and $\mathcal{P}=\{h\}$ for $1\leq h\leq k-1$. First, we derive the parity check matrix of $\mathcal{C}_h$ and provide a necessary and sufficient condition for $\mathcal{C}_h$ to be an AMDS code. Then, we construct two classes of LCD codes from $\mathcal{C}_h$ by suitably choosing the evaluation points together with certain restrictions on the coefficient of $x^{h-1}$ in the polynomial associated with the twisting term. From the constructed LCD codes we further obtain two classes of LCD MDS codes. Finally, several examples are presented.

翻译：扭曲广义Reed-Solomon（TGRS）码作为经典广义Reed-Solomon（GRS）码的灵活扩展，近年来受到广泛关注。本文从长度为$n$、维数为$k$的$(\mathcal{L},\mathcal{P})$-TGRS码$\mathcal{C}_h$构造了两类LCD码，其中$\mathcal{L}=\{0,1,\ldots,l\}$（满足$l\leq n-k-1$）且$\mathcal{P}=\{h\}$（满足$1\leq h\leq k-1$）。首先，我们推导出$\mathcal{C}_h$的校验矩阵，并给出$\mathcal{C}_h$成为AMDS码的充要条件。随后，通过适当选取评估点并对扭曲项关联多项式中$x^{h-1}$的系数施加特定约束，从$\mathcal{C}_h$构造出两类LCD码。基于所构造的LCD码，我们进一步获得了两类LCD MDS码。最后，文中给出了若干具体实例。