{"id":"https://openalex.org/W2121108343","doi":"https://doi.org/10.1142/s1793830912500309","title":"CODING THEORY ON h(x) FIBONACCI p-NUMBERS POLYNOMIALS","display_name":"CODING THEORY ON h(x) FIBONACCI p-NUMBERS POLYNOMIALS","publication_year":2012,"publication_date":"2012-08-06","ids":{"openalex":"https://openalex.org/W2121108343","doi":"https://doi.org/10.1142/s1793830912500309","mag":"2121108343"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500309","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500309","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110280536","display_name":"Manjusri Basu","orcid":null},"institutions":[{"id":"https://openalex.org/I77501641","display_name":"University of Kalyani","ror":"https://ror.org/03v783k16","country_code":"IN","type":"education","lineage":["https://openalex.org/I77501641"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"MANJUSRI BASU","raw_affiliation_strings":["Department of Mathematics, University of Kalyani, Kalyani - 741235, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kalyani, Kalyani - 741235, India","institution_ids":["https://openalex.org/I77501641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021778220","display_name":"Bandhu Prasad","orcid":"https://orcid.org/0000-0002-0439-8146"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"BANDHU PRASAD","raw_affiliation_strings":["Department of Mathematics, Kandi Raj College, Kandi - 742137, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kandi Raj College, Kandi - 742137, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110280536"],"corresponding_institution_ids":["https://openalex.org/I77501641"],"apc_list":null,"apc_paid":null,"fwci":0.4851,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65823269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"04","issue":"03","first_page":"1250030","last_page":"1250030"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14500","display_name":"Advanced Mathematical Theories","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.9510648846626282},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6324162483215332},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6321364641189575},{"id":"https://openalex.org/keywords/fibonacci-polynomials","display_name":"Fibonacci polynomials","score":0.5783786177635193},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.5717694163322449},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5399953722953796},{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.5344725251197815},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49732163548469543},{"id":"https://openalex.org/keywords/integer-matrix","display_name":"Integer matrix","score":0.4879454970359802},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4677543640136719},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16757410764694214},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.1279960572719574},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.11491578817367554},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.10840126872062683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09165555238723755},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.08486589789390564},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05254489183425903}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9510648846626282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6324162483215332},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6321364641189575},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.5783786177635193},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.5717694163322449},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5399953722953796},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.5344725251197815},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49732163548469543},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.4879454970359802},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4677543640136719},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16757410764694214},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.1279960572719574},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.11491578817367554},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.10840126872062683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09165555238723755},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.08486589789390564},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05254489183425903},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830912500309","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500309","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1965349501","https://openalex.org/W1969852862","https://openalex.org/W2019073482","https://openalex.org/W2030221505","https://openalex.org/W2065593776","https://openalex.org/W2074354445","https://openalex.org/W2079415843","https://openalex.org/W2123904937","https://openalex.org/W2172116884","https://openalex.org/W2476904967","https://openalex.org/W4254754212"],"related_works":["https://openalex.org/W2044513706","https://openalex.org/W2949398872","https://openalex.org/W4367677720","https://openalex.org/W2333479611","https://openalex.org/W2008022028","https://openalex.org/W3113738643","https://openalex.org/W2354266039","https://openalex.org/W3173275317","https://openalex.org/W4318214272","https://openalex.org/W2261462782"],"abstract_inverted_index":{"In":[0,135],"this":[1,140],"paper,":[2],"we":[3,37],"introduce":[4],"h(x)":[5,18,86,118,152],"Fibonacci":[6,12,19,108,132],"p-numbers":[7,20],"polynomials":[8,21],"and":[9,27,46,71],"a":[10,31,154],"new":[11],"Q":[13,42,53],"p,h":[14,43,54],"(x)":[15,44,55],"matrix":[16,45,64,83,98,115,129],"for":[17,66,85,100,117,131],"where":[22],"p(>":[23,67],"0)":[24,29,68],"is":[25,30,69,143],"integer":[26,70],"h(x)(>":[28,72],"polynomial":[32],"with":[33,92,122],"real":[34],"coefficients.":[35],"Thereby,":[36],"discuss":[38],"various":[39],"properties":[40],"of":[41,106,139,145],"the":[47,52,59,62,78,81,93,96,104,107,113,123,127,157],"coding":[48,101,133],"theory":[49,102],"followed":[50],"from":[51],"matrix.":[56],"We":[57,74],"establish":[58],"relations":[60,94,111,125],"among":[61,80,95,112,126],"code":[63,82,97,114,128],"elements":[65,84,99,116,130],"0).":[73],"also":[75],"show":[76],"that":[77],"relations,":[79],"=":[87,119],"m":[88],"(>":[89],"0),":[90],"coincide":[91,121],"on":[103],"m-extension":[105],"p-numbers.":[109],"The":[110],"1,":[120],"generalized":[124],"theory.":[134],"general,":[136],"correct":[137],"ability":[138],"method,":[141],"which":[142],"independent":[144],"h(x),":[146],"increases":[147,150],"as":[148],"p":[149],"but":[151],"being":[153],"polynomial,":[155],"improves":[156],"cryptography":[158],"protection.":[159]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}