{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T16:54:03Z","timestamp":1763830443444},"reference-count":26,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> In this paper, we define (m, t)-extension of the Fibonacci p-numbers and Golden (p, m, t)-proportions, where p \u2265 0 is integer, m &gt; 0, and t &gt; 0. We establish a relation among golden (p, m, t)-proportion, golden (p, m)-proportion and golden p-proportion. Thereby, we define a new Fibonacci G<jats:sub>p, m, t<\/jats:sub> matrix. Then we show that by proper selection of the initial terms for the (m, t)-extension of the Fibonacci p-numbers, we can apply Fibonacci coding\/decoding in G<jats:sub>p, m, t<\/jats:sub> matrix. Also it is obvious that for t = 1, the relations among the code elements for all values of p (non-negative integer) and m (&gt; 0) coincide with the relations among the code matrix elements for all values of p and m (&gt; 0) with the same initial terms (see the paper coding theory on the m-extension of the Fibonacci p-numbers, Chaos, Solitons and Fractals42 (2009) 2522\u20132530). <\/jats:p>","DOI":"10.1142\/s1793830911001097","type":"journal-article","created":{"date-parts":[[2011,7,13]],"date-time":"2011-07-13T09:20:39Z","timestamp":1310548839000},"page":"259-267","source":"Crossref","is-referenced-by-count":13,"title":["CODING THEORY ON THE (m, t)-EXTENSION OF THE FIBONACCI p-NUMBERS"],"prefix":"10.1142","volume":"03","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, West Bengal, 742137, India"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"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","volume-title":"The Golden Section and Non-Euclidean Geometry in Nature and Art","author":"Bodnar O. 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