A comparison of distance bounds for quasi-twisted codes

• 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
• Institution: Nanyang Technological University

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.