IEEE TRANSACTIONS ON INFORMATION THEORY, vol.67, no.10, pp.6476-6490, 2021 (SCI-Expanded)
Article / Article
IEEE TRANSACTIONS ON INFORMATION THEORY
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Eigenvalues and eigenfunctions, Manganese, Spectral analysis, Scholarships, Indexes, Generators, Product codes, Quasi-twisted code, concatenated code, minimum distance bound, polynomial matrices, spectral analysis, MINIMUM DISTANCE
Middle East Technical University Affiliated:
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.