English

A Comparison of Distance Bounds for Quasi-Twisted Codes

Information Theory 2021-05-25 v2 math.IT

Abstract

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.

Keywords

Cite

@article{arxiv.2012.10081,
  title  = {A Comparison of Distance Bounds for Quasi-Twisted Codes},
  author = {Martianus Frederic Ezerman and John Mark Lampos and San Ling and Buket Ozkaya and Jareena Tharnnukhroh},
  journal= {arXiv preprint arXiv:2012.10081},
  year   = {2021}
}