{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:39:01Z","timestamp":1767109141833,"version":"3.41.2"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"name":"School of Science, University of Phayao","award":["PBTSC64017"],"award-info":[{"award-number":["PBTSC64017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,10]]},"abstract":"<jats:p>This paper focuses on the matrix sequences that represent negative indices Pell and Pell\u2013Lucas number. It will specifically provide the important relationships between negative indices Pell and Pell\u2013Lucas number and Pell and Pell\u2013Lucas matrix sequences. The research of new error correcting codes has received a lot of attention in recent years, specifically due to its potential use in quantum-resistant cryptosystems. These matrices are then applied in cryptology and have a great opportunity to report some cases that might be a mistake between the sender and the receiver by using Lucas blocking algorithm.<\/jats:p>","DOI":"10.1142\/s1793830922501543","type":"journal-article","created":{"date-parts":[[2022,9,2]],"date-time":"2022-09-02T03:02:17Z","timestamp":1662087737000},"source":"Crossref","is-referenced-by-count":1,"title":["On matrix sequences represented by negative indices Pell and Pell\u2013Lucas number with the decoding of Lucas blocking error correcting codes"],"prefix":"10.1142","volume":"15","author":[{"given":"Kannika","family":"Khompurngson","sequence":"first","affiliation":[{"name":"Division of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand"}]},{"given":"Supunnee","family":"Sompong","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science and Technology, Sakon Nakhon Rajabhat University, Sakon Nakhon 47000, Thailand"}]}],"member":"219","published-online":{"date-parts":[[2022,10,4]]},"reference":[{"key":"S1793830922501543BIB001","first-page":"161","volume":"87","author":"Civciv H.","year":"2008","journal-title":"Ars Combin."},{"key":"S1793830922501543BIB002","first-page":"271","volume":"89","author":"Civciv H.","year":"2008","journal-title":"Ars Combin."},{"issue":"64","key":"S1793830922501543BIB003","first-page":"3173","volume":"5","author":"Dasdemir A.","year":"2011","journal-title":"Appl. Math. Sci."},{"issue":"10","key":"S1793830922501543BIB004","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1016\/j.aml.2012.01.014","volume":"25","author":"Gulec H. H.","year":"2012","journal-title":"Appl. Math. Lett."},{"issue":"3","key":"S1793830922501543BIB005","first-page":"245","volume":"9","author":"Horadam A. F.","year":"1971","journal-title":"Fibonacci Quart."},{"issue":"1","key":"S1793830922501543BIB006","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1080\/00150517.1985.12429849","volume":"23","author":"Horadam A. F.","year":"1985","journal-title":"Fibonacci Quart."},{"key":"S1793830922501543BIB007","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-8489-9","volume-title":"Pell and Pell-Lucas Numbers with Applications","author":"Koshy T.","year":"2014"},{"issue":"1","key":"S1793830922501543BIB008","doi-asserted-by":"crossref","first-page":"62","DOI":"10.36753\/mathenot.559251","volume":"7","author":"U\u00e7ar S.","year":"2019","journal-title":"Math. Sci. Appl. E-Notes"},{"key":"S1793830922501543BIB009","first-page":"381","volume-title":"Numerical Analysis and Applied Mathematics ICNAAM 2011 AIP Conf. Proc.","volume":"1389","author":"Yazlik Y.","year":"2011"},{"issue":"2","key":"S1793830922501543BIB010","first-page":"59","volume":"5","author":"Yilmaz N.","year":"2014","journal-title":"Commun. Math. Appl."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922501543","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T03:31:59Z","timestamp":1727926319000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922501543"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,4]]},"references-count":10,"journal-issue":{"issue":"07","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["10.1142\/S1793830922501543"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922501543","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,10,4]]},"article-number":"2250154"}}