New Quantum and LCD Codes Over the Finite Field of Odd Characteristic

In this paper, we study cyclic codes over a finite non-chain ring F p m + v F p m with v 2 = 1 and find new and better quantum error-correcting codes than previously known quantum error correcting codes over F p m . Therewith, we characterize the LCD codes and obtain many new LCD codes. Also, we pro...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	International journal of theoretical physics 2021-06, Vol.60 (6), p.2322-2332
Hauptverfasser:	Ashraf, Mohammad, Khan, Naim, Mohammad, Ghulam
Format:	Artikel
Sprache:	eng
Schlagworte:	Binary system Codes Elementary Particles Error correcting codes Error correction Error correction & detection Fields (mathematics) Mathematical and Computational Physics Physics Physics and Astronomy Quantum Field Theory Quantum Physics Theoretical
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	In this paper, we study cyclic codes over a finite non-chain ring F p m + v F p m with v 2 = 1 and find new and better quantum error-correcting codes than previously known quantum error correcting codes over F p m . Therewith, we characterize the LCD codes and obtain many new LCD codes. Also, we prove that the Gray map of an LCD code of length n over F p m + v F p m is an LCD code of length 2 n over F p m .
ISSN:	0020-7748 1572-9575
DOI:	10.1007/s10773-021-04849-2