We investigate a natural subfamily of twisted linearized Reed--Solomon (TLRS) codes in the sum-rank metric, where the twist is applied only to the constant term. We establish a simple necessary and sufficient condition for these codes to be linear complementary dual (LCD): the twisting parameter \(η\) must satisfy \(η^2 \neq -1\) in the underlying field. This criterion is independent of the evaluation subgroup, the dimension parameter, and the twisting exponent (subject only to a mild restriction on the code length). Furthermore, we construct infinite families of additive twisted linearized Reed--Solomon codes that are simultaneously additive complementary dual (ACD) and maximum distance separable (MDS) over quadratic extensions \(\mathbb{F}_{q^2}\), with respect to the trace-Hermitian inner product. These codes are explicit and achieve optimal parameters for all admissible lengths.

翻译：我们研究了和-秩度量下扭结线性化Reed–Solomon(TLRS)码的一个自然子类，其中扭结仅作用于常数项。我们建立了这些码为线性互补对偶(LCD)的简单充要条件：扭结参数\(η\)必须满足基础域中\(η^2 \neq -1\)。该判据独立于求值子群、维数参数和扭结指数（仅受码长的温和限制）。此外，我们构造了无限族可加扭结线性化Reed–Solomon码，它们在二次扩张\(\mathbb{F}_{q^2}\)上关于迹-厄米内积同时为可加互补对偶(ACD)和最大距离可分(MDS)。这些码是显式的，并在所有允许长度上达到最优参数。