Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory

A.P. Stakhov

Chaos, Solitons & Fractals, 2006, vol. 30, issue 1, 56-66

Abstract: We consider a new class of square Fibonacci (p+1)×(p+1)-matrices, which are based on the Fibonacci p-numbers (p=0,1,2,3,…), with a determinant equal to +1 or −1. This unique property leads to a generalization of the “Cassini formula” for Fibonacci numbers. An original Fibonacci coding/decoding method follows from the Fibonacci matrices. In contrast to classical redundant codes a basic peculiarity of the method is that it allows to correct matrix elements that can be theoretically unlimited integers. For the simplest case the correct ability of the method is equal 93.33% which exceeds essentially all well-known correcting codes.

Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077906000117
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:30:y:2006:i:1:p:56-66

DOI: 10.1016/j.chaos.2005.12.054

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().