Spectral bounds on the minimum distance of quasi-twisted codes over finite fields are proposed, based on eigenvalues of polynomial matrices and the corresponding eigenspaces. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a way similar to how the Roos and shift bounds extend the BCH and HT bounds for cyclic codes. The eigencodes of a quasi-twisted code in the spectral theory and the outer codes in its concatenated structure are related. A comparison based on this relation verifies that the Jensen bound always outperforms the spectral bound under special conditions, which yields a similar relation between the Lally and the spectral bounds. The performances of the Lally, Jensen and spectral bounds are presented in comparison with each other.
翻译：根据多面基体和相应的天平空间的等值值,提出了关于对有限域的准交错代码最低距离的光谱线条。这些光谱线条和Zeh-Ling线条以类似于 Roos 和 移动线条如何扩展 BCH 和 HT 圆形码线的方式对Semenov-Trifonov 和 Zeh-Ling 线条进行概括。光谱理论中的准交错代码和相连接结构的外源代码是相关的。基于这一关系进行的比较证实,詹森在特殊条件下总是超越光谱系,从而得出Lally 和光谱系之间的类似关系。Lally 、 Jensen 和光谱系的性能是相互比较的。
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