Semenov and Trifonov [22] developed a spectral theory for quasi-cyclic codes and formulated a BCH-like minimum distance bound. Their approach was generalized by Zeh and Ling [24], by using the HT bound. The first spectral bound for quasi-twisted codes appeared in [7], which generalizes Semenov-Trifonov and Zeh-Ling bounds, but its overall performance was observed to be worse than the Jensen bound. More recently, an improved spectral bound for quasi-cyclic codes was proposed in [15], which outperforms the Jensen bound in many cases. In this paper, we adopt this approach to quasi-twisted case and we show that this new generalized spectral bound provides tighter lower bounds on the minimum distance compared to the Jensen and Ezerman et. al. bounds.

翻译：Semenov与Trifonov[22]为拟循环码建立了谱理论，并提出了类BCH最小距离界。Zeh和Ling[24]通过运用HT界推广了该方法。针对拟扭码的首个谱界出现在文献[7]中，该结果推广了Semenov-Trifonov界与Zeh-Ling界，但其整体性能被观察到弱于Jensen界。近期，文献[15]提出了一种改进的拟循环码谱界，其在多数情况下优于Jensen界。本文将该方法拓展至拟扭码情形，并证明相较于Jensen界及Ezerman等人提出的界，这一新的广义谱界能为最小距离提供更紧致的下界。