{"id":"https://openalex.org/W4411336976","doi":"https://doi.org/10.1109/access.2025.3579919","title":"An Integer Erasure Correction Coding and Its Application for Security Enhancement of Encryption","display_name":"An Integer Erasure Correction Coding and Its Application for Security Enhancement of Encryption","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4411336976","doi":"https://doi.org/10.1109/access.2025.3579919"},"language":"en","primary_location":{"id":"doi:10.1109/access.2025.3579919","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3579919","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2025.3579919","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020416375","display_name":"Miodrag J. Mihaljevi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Miodrag J. Mihaljevi\u0107","raw_affiliation_strings":["Key Laboratory of Computing Power Network and Information Security, Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan, China"],"raw_orcid":"https://orcid.org/0000-0003-3047-3020","affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing Power Network and Information Security, Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]},{"raw_affiliation_string":"Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010797340","display_name":"Aleksandar Radonji\u0107","orcid":"https://orcid.org/0000-0003-3715-468X"},"institutions":[{"id":"https://openalex.org/I1338511612","display_name":"Serbian Academy of Sciences and Arts","ror":"https://ror.org/05m1y4204","country_code":"RS","type":"government","lineage":["https://openalex.org/I1338511612"]},{"id":"https://openalex.org/I4210117138","display_name":"Institute of Technical Sciences of SASA","ror":"https://ror.org/02f2wk572","country_code":"RS","type":"facility","lineage":["https://openalex.org/I1338511612","https://openalex.org/I4210117138"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Aleksandar Radonji\u0107","raw_affiliation_strings":["Institute of Technical Sciences, Serbian Academy of Sciences and Arts, Belgrade, Serbia","Institute of Technical Sciences, Serbian Academy of Sciences and Arts, Kneza Mihaila 35, Belgrade, Serbia"],"raw_orcid":"https://orcid.org/0000-0003-3715-468X","affiliations":[{"raw_affiliation_string":"Institute of Technical Sciences, Serbian Academy of Sciences and Arts, Belgrade, Serbia","institution_ids":["https://openalex.org/I1338511612","https://openalex.org/I4210117138"]},{"raw_affiliation_string":"Institute of Technical Sciences, Serbian Academy of Sciences and Arts, Kneza Mihaila 35, Belgrade, Serbia","institution_ids":["https://openalex.org/I1338511612","https://openalex.org/I4210117138"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014839725","display_name":"Nevena Mijajlovi\u0107","orcid":"https://orcid.org/0000-0001-6792-1435"},"institutions":[{"id":"https://openalex.org/I5936373","display_name":"University of Montenegro","ror":"https://ror.org/02drrjp49","country_code":"ME","type":"education","lineage":["https://openalex.org/I5936373"]}],"countries":["ME"],"is_corresponding":false,"raw_author_name":"Nevena Mijajlovi\u0107","raw_affiliation_strings":["Faculty of Science and Mathematics, University of Montenegro, Podgorica, Montenegro","Faculty of Science and Mathematics, University of Montenegro, Džordža Vašingtona bb, Podgorica, Montenegro"],"raw_orcid":"https://orcid.org/0000-0001-6792-1435","affiliations":[{"raw_affiliation_string":"Faculty of Science and Mathematics, University of Montenegro, Podgorica, Montenegro","institution_ids":["https://openalex.org/I5936373"]},{"raw_affiliation_string":"Faculty of Science and Mathematics, University of Montenegro, Džordža Vašingtona bb, Podgorica, Montenegro","institution_ids":["https://openalex.org/I5936373"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005738289","display_name":"Lianhai Wang","orcid":"https://orcid.org/0000-0002-5701-3465"},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lianhai Wang","raw_affiliation_strings":["Key Laboratory of Computing Power Network and Information Security, Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-5701-3465","affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing Power Network and Information Security, Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]},{"raw_affiliation_string":"Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038014942","display_name":"Shujiang Xu","orcid":"https://orcid.org/0000-0001-9151-2834"},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shujiang Xu","raw_affiliation_strings":["Key Laboratory of Computing Power Network and Information Security, Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan, China"],"raw_orcid":"https://orcid.org/0000-0001-9151-2834","affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing Power Network and Information Security, Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]},{"raw_affiliation_string":"Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan, China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0641178,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":null,"first_page":"104728","last_page":"104741"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9635999798774719,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.95660001039505,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7604248523712158},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.6545148491859436},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.6381533145904541},{"id":"https://openalex.org/keywords/erasure-code","display_name":"Erasure code","score":0.5061044096946716},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4741995930671692},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4643701910972595},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3302115201950073},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32119524478912354},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.2649153470993042},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.26140716671943665},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.15887528657913208}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7604248523712158},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.6545148491859436},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.6381533145904541},{"id":"https://openalex.org/C137529215","wikidata":"https://www.wikidata.org/wiki/Q5385031","display_name":"Erasure code","level":3,"score":0.5061044096946716},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4741995930671692},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4643701910972595},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3302115201950073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32119524478912354},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.2649153470993042},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.26140716671943665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15887528657913208},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/access.2025.3579919","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3579919","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:dais.sanu.ac.rs:123456789/17958","is_oa":true,"landing_page_url":"https://dais.sanu.ac.rs/123456789/17958","pdf_url":null,"source":{"id":"https://openalex.org/S4306402581","display_name":"Digital Archive of SASA (Serbian Academy of Sciences and Arts)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1338511612","host_organization_name":"Serbian Academy of Sciences and Arts","host_organization_lineage":["https://openalex.org/I1338511612"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access","raw_type":"article"},{"id":"pmh:oai:doaj.org/article:dd1deeaa7ca54ef1ba44620614ea1c16","is_oa":true,"landing_page_url":"https://doaj.org/article/dd1deeaa7ca54ef1ba44620614ea1c16","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 13, Pp 104728-104741 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2025.3579919","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3579919","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1706370102","display_name":null,"funder_award_id":"ZR2023QF129","funder_id":"https://openalex.org/F4320334065","funder_display_name":"National Natural Science Foundation of China-Shandong Joint Fund"},{"id":"https://openalex.org/G2284860812","display_name":null,"funder_award_id":"62102209","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4111775640","display_name":null,"funder_award_id":"2023YFC3304903","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4488208638","display_name":null,"funder_award_id":"202228017","funder_id":"https://openalex.org/F4320329338","funder_display_name":"Independent Innovation Foundation of Higher Education of China"},{"id":"https://openalex.org/G5772542026","display_name":null,"funder_award_id":"F-153","funder_id":"https://openalex.org/F4320330165","funder_display_name":"Serbian Academy of Sciences and Arts"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329338","display_name":"Independent Innovation Foundation of Higher Education of China","ror":null},{"id":"https://openalex.org/F4320330165","display_name":"Serbian Academy of Sciences and Arts","ror":"https://ror.org/05m1y4204"},{"id":"https://openalex.org/F4320334065","display_name":"National Natural Science Foundation of China-Shandong Joint Fund","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W658016334","https://openalex.org/W1489829676","https://openalex.org/W1572614022","https://openalex.org/W1972808865","https://openalex.org/W1972831370","https://openalex.org/W1979510651","https://openalex.org/W1992506348","https://openalex.org/W2000599680","https://openalex.org/W2015867428","https://openalex.org/W2029226988","https://openalex.org/W2031335939","https://openalex.org/W2038315579","https://openalex.org/W2083709137","https://openalex.org/W2095767396","https://openalex.org/W2099294566","https://openalex.org/W2113333997","https://openalex.org/W2129077868","https://openalex.org/W2140655888","https://openalex.org/W2150498905","https://openalex.org/W2157145873","https://openalex.org/W2163452843","https://openalex.org/W2166849128","https://openalex.org/W2184713351","https://openalex.org/W2296082067","https://openalex.org/W2330890468","https://openalex.org/W2348697673","https://openalex.org/W2392237044","https://openalex.org/W2531377551","https://openalex.org/W2561049596","https://openalex.org/W2574162063","https://openalex.org/W2588432628","https://openalex.org/W2742366887","https://openalex.org/W2762962924","https://openalex.org/W2775671069","https://openalex.org/W2885790886","https://openalex.org/W2886594662","https://openalex.org/W2905683382","https://openalex.org/W2910760155","https://openalex.org/W2923015260","https://openalex.org/W2950353718","https://openalex.org/W2962277667","https://openalex.org/W2963473550","https://openalex.org/W2966075018","https://openalex.org/W3000170011","https://openalex.org/W3026492770","https://openalex.org/W3030897411","https://openalex.org/W3037522227","https://openalex.org/W3132442727","https://openalex.org/W4207034359","https://openalex.org/W4220701981","https://openalex.org/W4226284548","https://openalex.org/W4292266502","https://openalex.org/W4300349690","https://openalex.org/W4307238902","https://openalex.org/W4361801137","https://openalex.org/W4378909289","https://openalex.org/W4381732728","https://openalex.org/W4391164237","https://openalex.org/W4405950648"],"related_works":["https://openalex.org/W2982181605","https://openalex.org/W2130518071","https://openalex.org/W2137028263","https://openalex.org/W2115768470","https://openalex.org/W1694938350","https://openalex.org/W2744779861","https://openalex.org/W3184492641","https://openalex.org/W2031335939","https://openalex.org/W2951344115","https://openalex.org/W969204977"],"abstract_inverted_index":{"This":[0,120],"paper":[1],"presents":[2],"a":[3,67,80,95],"new":[4],"class":[5],"of":[6,15,132],"erasure-correcting":[7],"codes":[8],"(ECCs)":[9],"aimed":[10],"at":[11],"enhancing":[12],"cryptographic":[13],"security":[14],"certain":[16,133],"encryption":[17,46,54],"schemes.":[18],"The":[19,58],"proposed":[20,64],"ECCs":[21,65],"employ":[22],"integer":[23],"arithmetic":[24],"to":[25],"encode":[26],"and":[27,31,66,102,136],"decode":[28],"data":[29,35],"bits":[30],"can":[32],"correct":[33],"all":[34],"bytes,":[36],"each":[37],"affected":[38],"by":[39,51,139],"exactly":[40],"two":[41,115],"erasures..":[42],"In":[43],"the":[44,48,52,63,74,89,105,109,130],"enhanced":[45],"scheme,":[47],"ciphertext":[49],"produced":[50],"initial":[53],"undergoes":[55],"further":[56],"processing.":[57],"enhancement":[59],"leverages":[60],"specific":[61],"fragmentation,":[62],"simulated":[68,75],"noisy":[69,76],"channel.":[70],"For":[71],"legitimate":[72],"users,":[73],"channel":[77,96],"functions":[78],"as":[79,94],"binary":[81],"erasure":[82],"channel,":[83],"while":[84],"for":[85],"an":[86],"attacker":[87],"without":[88],"secret":[90],"key,":[91],"it":[92],"acts":[93],"with":[97],"random":[98,118],"deletions.":[99],"Security":[100],"notation":[101],"evaluation":[103,121],"follow":[104],"traditional":[106],"approach,":[107],"assessing":[108],"attacker\u2019s":[110],"advantage":[111],"in":[112],"distinguishing":[113],"between":[114],"ciphertexts":[116],"versus":[117],"guessing.":[119],"employs":[122],"dedicated":[123],"analysis":[124],"based":[125],"on":[126,129],"information-theoretic":[127],"findings":[128],"capacity":[131],"deletion":[134],"channels":[135],"is":[137],"supported":[138],"illustrative":[140],"numerical":[141],"examples.":[142]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}