{"id":"https://openalex.org/W4406962323","doi":"https://doi.org/10.26493/1855-3974.3336.b06","title":"The minimum weight of the code of intersecting lines in PG(3,q)","display_name":"The minimum weight of the code of intersecting lines in PG(3,q)","publication_year":2025,"publication_date":"2025-01-30","ids":{"openalex":"https://openalex.org/W4406962323","doi":"https://doi.org/10.26493/1855-3974.3336.b06"},"language":"en","primary_location":{"id":"doi:10.26493/1855-3974.3336.b06","is_oa":true,"landing_page_url":"https://doi.org/10.26493/1855-3974.3336.b06","pdf_url":"https://amc-journal.eu/index.php/amc/article/download/3336/2142","source":{"id":"https://openalex.org/S61442588","display_name":"Ars Mathematica Contemporanea","issn_l":"1855-3966","issn":["1855-3966","1855-3974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310314472","host_organization_name":"Society of Mathematicians, Physicists and Astronomers of Slovenia","host_organization_lineage":["https://openalex.org/P4310314472"],"host_organization_lineage_names":["Society of Mathematicians, Physicists and Astronomers of Slovenia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Mathematica Contemporanea","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://amc-journal.eu/index.php/amc/article/download/3336/2142","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031469231","display_name":"Sam Adriaensen","orcid":"https://orcid.org/0000-0002-0925-9305"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Sam Adriaensen","raw_affiliation_strings":["Vrije Universiteit Brussel, Belgium and Worcester Polytechnic Institute, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Brussel, Belgium and Worcester Polytechnic Institute, United States","institution_ids":["https://openalex.org/I13469542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069446671","display_name":"Robin Simoens","orcid":"https://orcid.org/0000-0001-7398-3085"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Robin Simoens","raw_affiliation_strings":["Ghent University, Belgium and Universitat Polit\u00e8cnica de Catalunya, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ghent University, Belgium and Universitat Polit\u00e8cnica de Catalunya, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061433215","display_name":"Leo Storme","orcid":"https://orcid.org/0000-0001-6440-9225"},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Leo Storme","raw_affiliation_strings":["Ghent University, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ghent University, Belgium","institution_ids":["https://openalex.org/I2801227569"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031469231"],"corresponding_institution_ids":["https://openalex.org/I13469542"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00627096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"1","first_page":"#P1.01","last_page":"#P1.01"},"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":0.9962999820709229,"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/T10849","display_name":"Finite Group Theory Research","score":0.9724000096321106,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.8668530583381653},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6470275521278381},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5644002556800842},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3318067789077759},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05823129415512085},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.05574861168861389},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.053105831146240234}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8668530583381653},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6470275521278381},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5644002556800842},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3318067789077759},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05823129415512085},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.05574861168861389},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.053105831146240234}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.26493/1855-3974.3336.b06","is_oa":true,"landing_page_url":"https://doi.org/10.26493/1855-3974.3336.b06","pdf_url":"https://amc-journal.eu/index.php/amc/article/download/3336/2142","source":{"id":"https://openalex.org/S61442588","display_name":"Ars Mathematica Contemporanea","issn_l":"1855-3966","issn":["1855-3966","1855-3974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310314472","host_organization_name":"Society of Mathematicians, Physicists and Astronomers of Slovenia","host_organization_lineage":["https://openalex.org/P4310314472"],"host_organization_lineage_names":["Society of Mathematicians, Physicists and Astronomers of Slovenia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Mathematica Contemporanea","raw_type":"journal-article"},{"id":"pmh:oai:upcommons.upc.edu:2117/460543","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/460543","pdf_url":"https://upcommons.upc.edu/bitstreams/ad60b15e-627b-4d0e-af2d-ddfa4a7cb24f/download","source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:archive.ugent.be:01JN3ZH65JRNT4TG663S0M7GW3","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-01JN3ZH65JRNT4TG663S0M7GW3","pdf_url":"https://biblio.ugent.be/publication/01JN3ZH65JRNT4TG663S0M7GW3/file/01KCTV7R5G8PCRDXB1MHFPCRQN.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"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":"ISSN: 1855-3974","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:vubissmart:VUBISSMART:2000:259675","is_oa":false,"landing_page_url":"https://biblio.vub.ac.be/vubir/the-minimum-weight-of-the-code-of-intersecting-lines-in-pg3q(15b9a07a-4718-434d-8036-8cc829dd1297).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402573","display_name":"VUBIR (Vrije Universiteit Brussel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13469542","host_organization_name":"Vrije Universiteit Brussel","host_organization_lineage":["https://openalex.org/I13469542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"}],"best_oa_location":{"id":"doi:10.26493/1855-3974.3336.b06","is_oa":true,"landing_page_url":"https://doi.org/10.26493/1855-3974.3336.b06","pdf_url":"https://amc-journal.eu/index.php/amc/article/download/3336/2142","source":{"id":"https://openalex.org/S61442588","display_name":"Ars Mathematica Contemporanea","issn_l":"1855-3966","issn":["1855-3966","1855-3974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310314472","host_organization_name":"Society of Mathematicians, Physicists and Astronomers of Slovenia","host_organization_lineage":["https://openalex.org/P4310314472"],"host_organization_lineage_names":["Society of Mathematicians, Physicists and Astronomers of Slovenia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Mathematica Contemporanea","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8046143882","display_name":null,"funder_award_id":"11PG724N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320306621","display_name":"Belgian American Educational Foundation","ror":"https://ror.org/014rsed66"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406962323.pdf","grobid_xml":"https://content.openalex.org/works/W4406962323.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0],"characterise":[1,61],"the":[2,7,30,45,62],"minimum":[3,31,46],"weight":[4,32,47],"codewords":[5,63],"of":[6,11,64],"p-ary":[8],"linear":[9],"code":[10],"intersecting":[12],"lines":[13],"in":[14],"PG(3,q),":[15],"q":[16,19,27,38,42,53,57],"=":[17],"ph,":[18],"\u2265":[20,24],"19,":[21],"p":[22],"prime,h":[23],"1.":[25,40,55],"If":[26,41],"is":[28,43],"even,":[29,58],"equals":[33,48],"q\u00b3":[34,49],"+":[35,37,39,50,52,54],"q\u00b2":[36],"odd,":[44],"2q\u00b2":[51],"For":[56],"we":[59],"also":[60],"second":[65],"smallest":[66],"weight.":[67]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
