A Comparison of Distance Bounds for Quasi-Twisted Codes

Date

2021-10-01

Author

Ezerman, Martianus Frederic
Lampos, John Mark
Ling, San
Özkaya, Buket
Tharnnukhroh, Jareena

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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.

Subject Keywords

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

URI

https://hdl.handle.net/11511/104005

Collections

Graduate School of Applied Mathematics, Article