Skew Constacyclic Codes over a Family of Finite Rings and Their Applications to LCD and Quantum Codes

Dertli, Abdullah

doi:10.1007/s11401-025-0052-x

Skew Constacyclic Codes over a Family of Finite Rings and Their Applications to LCD and Quantum Codes

Dertli A.

CHINESE ANNALS OF MATHEMATICS SERIES B, 2025 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Basım Tarihi: 2025
Doi Numarası: 10.1007/s11401-025-0052-x
Dergi Adı: CHINESE ANNALS OF MATHEMATICS SERIES B
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

This paper studies skew constacyclic codes over a family of finite rings denoted by Bk to obtain quantum codes over the fields \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_{p<^>r}$$\end{document} and to construct Euclidean LCD skew constacyclic codes. The author investigates the structural properties of skew constacyclic codes over Bk using a decomposition approach, and also finds necessary and sufficient conditions for skew constacyclic codes that contain their duals. Finally, the author gives some examples of quantum codes obtained via the construction and LCD codes.