Generalized spectral bound for quasi-twisted codes
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.
Fields of Study & Subjects
Coding theory and cryptography
graph theory and CDMA systems
Error Correcting Code Techniques
Publication details
- Journal / source
- TURKISH JOURNAL OF MATHEMATICS
- Publisher
- The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALS
- Volume
- 50
- Issue
- 5
- Pages
- 842–860
- Publication date
- 1 September 2026
- Language
- EN