  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.
