{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T22:25:32Z","timestamp":1706135132239},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> In this paper, we introduce h(x) Fibonacci p-numbers polynomials and a new Fibonacci Q<jats:sub>p,h<\/jats:sub>(x) matrix for h(x) Fibonacci p-numbers polynomials where p(&gt; 0) is integer and h(x)(&gt; 0) is a polynomial with real coefficients. Thereby, we discuss various properties of Q<jats:sub>p,h<\/jats:sub>(x) matrix and the coding theory followed from the Q<jats:sub>p,h<\/jats:sub>(x) matrix. We establish the relations among the code matrix elements for p(&gt; 0) is integer and h(x)(&gt; 0). We also show that the relations, among the code matrix elements for h(x) = m (&gt; 0), coincide with the relations among the code matrix elements for coding theory on the m-extension of the Fibonacci p-numbers. The relations among the code matrix elements for h(x) = 1, coincide with the generalized relations among the code matrix elements for Fibonacci coding theory. In general, correct ability of this method, which is independent of h(x), increases as p increases but h(x) being a polynomial, improves the cryptography protection. <\/jats:p>","DOI":"10.1142\/s1793830912500309","type":"journal-article","created":{"date-parts":[[2012,8,6]],"date-time":"2012-08-06T08:31:23Z","timestamp":1344241883000},"page":"1250030","source":"Crossref","is-referenced-by-count":2,"title":["CODING THEORY ON h(x) FIBONACCI p-NUMBERS POLYNOMIALS"],"prefix":"10.1142","volume":"04","author":[{"given":"MANJUSRI","family":"BASU","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Kalyani, Kalyani - 741235, India"}]},{"given":"BANDHU","family":"PRASAD","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kandi Raj College, Kandi - 742137, India"}]}],"member":"219","published-online":{"date-parts":[[2012,8,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2008.09.030"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2009.03.197"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.04.043"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2008.09.059"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2009.01.007"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.03.007"},{"key":"rf7","volume-title":"Gnomon: From Pharaons to Fractals","author":"Gazale M. J.","year":"1999"},{"key":"rf8","volume-title":"Elementary Matrix Algebra","author":"Hohn F. E.","year":"1973"},{"key":"rf9","doi-asserted-by":"crossref","DOI":"10.1142\/4767","volume-title":"Beyond Measurement: A Guided Tour Through Nature, Myth and Number","author":"Kappraff J.","year":"2002"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.09.071"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2009.04.048"},{"key":"rf12","volume-title":"From the Golden Mean to Chaos","author":"Spinadel V. W.","year":"1998"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.12.054"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:43:33Z","timestamp":1565131413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,6]]},"references-count":13,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,8,6]]},"published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.1142\/S1793830912500309"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500309","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,6]]}}}