{"id":"https://openalex.org/W3134325355","doi":"https://doi.org/10.3390/e23030323","title":"Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding","display_name":"Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding","publication_year":2021,"publication_date":"2021-03-09","ids":{"openalex":"https://openalex.org/W3134325355","doi":"https://doi.org/10.3390/e23030323","mag":"3134325355","pmid":"https://pubmed.ncbi.nlm.nih.gov/33803220"},"language":"en","primary_location":{"id":"doi:10.3390/e23030323","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23030323","pdf_url":"https://www.mdpi.com/1099-4300/23/3/323/pdf?version=1616132155","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/3/323/pdf?version=1616132155","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100340169","display_name":"Qi Chen","orcid":"https://orcid.org/0000-0002-5322-4783"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Chen","raw_affiliation_strings":["State Key Laboratory of Integrated Service Networks, Xidian University, Xi\u2019 an 710071, China","State Key Laboratory of Integrated Service Networks, Xidian University, Xi' an 710071, China"],"raw_orcid":"https://orcid.org/0000-0002-5322-4783","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Integrated Service Networks, Xidian University, Xi\u2019 an 710071, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Service Networks, Xidian University, Xi' an 710071, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047438727","display_name":"Minquan Cheng","orcid":"https://orcid.org/0000-0003-0360-0610"},"institutions":[{"id":"https://openalex.org/I29739308","display_name":"Guangxi Normal University","ror":"https://ror.org/02frt9q65","country_code":"CN","type":"education","lineage":["https://openalex.org/I29739308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Minquan Cheng","raw_affiliation_strings":["Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China"],"raw_orcid":"https://orcid.org/0000-0003-0360-0610","affiliations":[{"raw_affiliation_string":"Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China","institution_ids":["https://openalex.org/I29739308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063124926","display_name":"Baoming Bai","orcid":"https://orcid.org/0000-0002-6161-5493"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Baoming Bai","raw_affiliation_strings":["State Key Laboratory of Integrated Service Networks, Xidian University, Xi\u2019 an 710071, China","State Key Laboratory of Integrated Service Networks, Xidian University, Xi' an 710071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Integrated Service Networks, Xidian University, Xi\u2019 an 710071, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Service Networks, Xidian University, Xi' an 710071, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047438727","https://openalex.org/A5063124926","https://openalex.org/A5100340169"],"corresponding_institution_ids":["https://openalex.org/I149594827","https://openalex.org/I29739308"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.782,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77100633,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"23","issue":"3","first_page":"323","last_page":"323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9995999932289124,"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/matroid","display_name":"Matroid","score":0.9671086668968201},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6446062326431274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.63145911693573},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.575194239616394},{"id":"https://openalex.org/keywords/oriented-matroid","display_name":"Oriented matroid","score":0.5525175333023071},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5018515586853027},{"id":"https://openalex.org/keywords/weighted-matroid","display_name":"Weighted matroid","score":0.49732163548469543},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.48641109466552734},{"id":"https://openalex.org/keywords/matroid-partitioning","display_name":"Matroid partitioning","score":0.47602230310440063},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4439116418361664},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.41237348318099976},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11580926179885864},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07359746098518372}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9671086668968201},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6446062326431274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.63145911693573},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.575194239616394},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.5525175333023071},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5018515586853027},{"id":"https://openalex.org/C124344645","wikidata":"https://www.wikidata.org/wiki/Q7979897","display_name":"Weighted matroid","level":5,"score":0.49732163548469543},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.48641109466552734},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.47602230310440063},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4439116418361664},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.41237348318099976},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11580926179885864},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07359746098518372},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23030323","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23030323","pdf_url":"https://www.mdpi.com/1099-4300/23/3/323/pdf?version=1616132155","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33803220","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33803220","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:e09fa15635264854b1d202266a79e3fb","is_oa":true,"landing_page_url":"https://doaj.org/article/e09fa15635264854b1d202266a79e3fb","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":"Entropy, Vol 23, Iss 3, p 323 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/3/323/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23030323","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 23; Issue 3; Pages: 323","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7999956","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7999956","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23030323","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23030323","pdf_url":"https://www.mdpi.com/1099-4300/23/3/323/pdf?version=1616132155","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1982178045","display_name":null,"funder_award_id":"61971321","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3134325355.pdf","grobid_xml":"https://content.openalex.org/works/W3134325355.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1014863066","https://openalex.org/W1520448495","https://openalex.org/W1525224470","https://openalex.org/W1555179723","https://openalex.org/W1970845455","https://openalex.org/W1992823229","https://openalex.org/W2000680242","https://openalex.org/W2028511489","https://openalex.org/W2031071287","https://openalex.org/W2031906711","https://openalex.org/W2038207731","https://openalex.org/W2038916015","https://openalex.org/W2091268429","https://openalex.org/W2113940092","https://openalex.org/W2131304595","https://openalex.org/W2140678653","https://openalex.org/W2148623656","https://openalex.org/W2167703619","https://openalex.org/W2545598615","https://openalex.org/W2733203216","https://openalex.org/W3102739603","https://openalex.org/W4205545339","https://openalex.org/W4249150173","https://openalex.org/W6740800177"],"related_works":["https://openalex.org/W2378157773","https://openalex.org/W2400862597","https://openalex.org/W1984819493","https://openalex.org/W2980228156","https://openalex.org/W4303709689","https://openalex.org/W1978795414","https://openalex.org/W2153065381","https://openalex.org/W2058489697","https://openalex.org/W2625145881","https://openalex.org/W2159059797"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,115],"study":[4],"the":[5,12,45,59,62,69,108,125],"entropy":[6,21,119],"functions":[7,120],"on":[8],"extreme":[9],"rays":[10],"of":[11,61,110,121,127],"polymatroidal":[13],"region":[14],"which":[15,39,92],"contain":[16],"a":[17,31,75],"matroid,":[18],"i.e.,":[19,80],"matroidal":[20,118],"functions.":[22],"We":[23],"introduce":[24],"variable":[25,111],"strength":[26,112],"orthogonal":[27,49,113],"arrays":[28],"indexed":[29],"by":[30],"connected":[32],"matroid":[33,63,83],"M":[34,64],"and":[35,68,87,105,129],"positive":[36],"integer":[37],"v":[38,67],"can":[40],"be":[41],"regarded":[42],"as":[43,102],"expanding":[44],"classic":[46],"combinatorial":[47,85],"structure":[48],"arrays.":[50],"It":[51],"is":[52,90],"interesting":[53],"that":[54],"they":[55],"are":[56],"equivalent":[57],"to":[58,95],"partition-representations":[60],"with":[65,124],"degree":[66],"(M,v)":[70],"almost":[71],"affine":[72],"codes.":[73],"Thus,":[74],"synergy":[76],"among":[77],"four":[78],"fields,":[79],"information":[81,99],"theory,":[82,84],"design,":[86],"coding":[88,104],"theory":[89],"developed,":[91],"may":[93],"lead":[94],"potential":[96],"applications":[97],"in":[98],"problems":[100],"such":[101],"network":[103],"secret-sharing.":[106],"Leveraging":[107],"construction":[109],"arrays,":[114],"characterize":[116],"all":[117],"order":[122],"n\u22645":[123],"exception":[126],"log10\u00b7U2,5":[128],"logv\u00b7U3,5":[130],"for":[131],"some":[132],"v.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}