The deep holes of a linear code are the vectors that achieve the maximum error distance to the code. There has been extensive research on the topic of deep holes in Reed-Solomon codes. As a generalization of Reed-Solomon codes, we investigate the problem of deep holes of a class of twisted Reed-Solomon codes in this paper. The covering radius and a standard class of deep holes of twisted Reed-Solomon codes ${\rm TRS}_k(\mathcal{A}, \theta)$ are obtained for a general evaluation set $\mathcal{A} \subseteq \mathbb{F}_q$. Furthermore, we consider the problem of determining all deep holes of the full-length twisted Reed-Solomon codes ${\rm TRS}_k(\mathbb{F}_q, \theta)$. Specifically, we prove that there are no other deep holes of ${\rm TRS}_k(\mathbb{F}_q, \theta)$ for $\frac{3q-8}{4} \leq k\leq q-4$ when $q$ is even, and $\frac{3q+2\sqrt{q}-7}{4} \leq k\leq q-4$ when $q$ is odd. We also completely determine their deep holes for $q-3 \leq k \leq q-1$.

翻译：线性码的深洞是到达该码的最大错误距离的向量。关于Reed-Solomon码的深洞问题已有广泛研究。作为Reed-Solomon码的推广，本文研究了一类扭曲Reed-Solomon码的深洞问题。对于一般评估集$\mathcal{A} \subseteq \mathbb{F}_q$，我们得到了扭曲Reed-Solomon码${\rm TRS}_k(\mathcal{A}, \theta)$的覆盖半径和一类标准深洞。进一步，我们考虑了确定全长扭曲Reed-Solomon码${\rm TRS}_k(\mathbb{F}_q, \theta)$的所有深洞的问题。具体地，我们证明：当$q$为偶数且$\frac{3q-8}{4} \leq k\leq q-4$时，以及当$q$为奇数且$\frac{3q+2\sqrt{q}-7}{4} \leq k\leq q-4$时，${\rm TRS}_k(\mathbb{F}_q, \theta)$不存在其他深洞。此外，我们还完全确定了$q-3 \leq k \leq q-1$情形下的深洞。