Codes over Graphs Derived from Quotient Rings of the Quaternion Orders. (27th June 2012)

• Record Type: Journal Article
• Authors: Quilles Queiroz, Cátia R. de O.; Palazzo Júnior, Reginaldo
• Other Names: Airault H. Academic Editor.; Milas A. Academic Editor.; You H. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2012(2012)
• Publication Date: 2012-06-27
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.5402/2012/956017
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : We propose the construction of signal space codes over the quaternion orders from a graph associated with the arithmetic Fuchsian group Γ 8 . This Fuchsian group consists of the edge-pairing isometries of the regular hyperbolic polygon (fundamental region) P 8, which tessellates the hyperbolic plane 𝔻 2 . Knowing the generators of the quaternion orders which realize the edge pairings of the polygon, the signal points of the signal constellation (geometrically uniform code) derived from the graph associated with the quotient ring of the quaternion order are determined.