A comparison of distance bounds for quasi-twisted codes

A comparison of distance bounds for quasi-twisted codes

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...

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Bibliographic Details
Main Authors: Ezerman, Martianus Frederic, Lampos, John Mark, Ling, San, Özkaya, Buket, Tharnnukhroh. Jareena
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Science::Mathematics::Applied mathematics::Information theory
Minimum Distance Bound
Quasi-Twisted Code
Online Access:https://hdl.handle.net/10356/155577
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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