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Turkish Journal of Mathematics

Author ORCID Identifier

BUKET ÖZKAYA: 0000-0003-2658-5441

Abstract

Minimum distance bounds play a central role in the analysis of algebraic codes. For cyclic and constacyclic codes, several bounds based on their zero set have been developed. However, analogous results for quasi-twisted (QT) codes are comparatively limited. In this paper, we further investigate the spectral theory of QT codes and derive a general spectral bound on their minimum distance. Our bound unifies and generalizes previously known spectral bounds for quasi-cyclic (QC) and QT codes, and contains them as special cases. We present a new proof technique and show that the bound can be formulated with respect to an arbitrary subset of eigenvalues, thereby extending its applicability to the largest possible setting. Numerical examples and simulations demonstrate that the proposed bound often improves upon the Jensen bound and earlier spectral bounds.

DOI

10.55730/1300-0098.3770

Keywords

Quasi-twisted code, concatenated code, spectral bound

First Page

842

Last Page

860

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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