Anzeige
Erschienen in:
24.09.2016 | Original Research
Cyclic DNA codes over \(\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2\) and their applications
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2017
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
In this paper, we study the structure of cyclic DNA codes of arbitrary length over the ring \(R=\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2\), \(u^{2}=0, v^{2}=v, uv=vu\). By defining a Gray map, we establish a relation between R and \(R^{2}_{1}\), where \(R_{1}=\mathbb {F}_2+u\mathbb {F}_2\) is a ring with four elements. Cyclic codes of arbitrary length over R satisfying the reverse constraint and the reverse-complement constraint are studied in this paper. Furthermore, we introduce reversible codes which provide a rich source for DNA codes. The GC content constraint is also considered. We give some examples to support our study in the last.