{"id":"https://openalex.org/W2944170798","doi":"https://doi.org/10.1007/s10623-019-00710-0","title":"Small weight code words arising from the incidence of points and hyperplanes in PG(n,q)","display_name":"Small weight code words arising from the incidence of points and hyperplanes in PG(n,q)","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2944170798","doi":"https://doi.org/10.1007/s10623-019-00710-0","mag":"2944170798"},"language":"en","primary_location":{"id":"pmh:oai:vubissmart:VUBISSMART:2000:127519","is_oa":false,"landing_page_url":"https://biblio.vub.ac.be/vubir/small-weight-code-words-arising-from-the-incidence-of-points-and-hyperplanes-in-pgnq(17d494df-732b-44b5-9853-624377cf02cb).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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":[],"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/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":false,"raw_author_name":"Sam Adriaensen","raw_affiliation_strings":["Department of Mathematics , Vrije Universiteit Brussel , Brussels , Belgium"],"raw_orcid":"https://orcid.org/0000-0002-0925-9305","affiliations":[{"raw_affiliation_string":"Department of Mathematics , Vrije Universiteit Brussel , Brussels , Belgium","institution_ids":["https://openalex.org/I13469542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011510161","display_name":"Lins Denaux","orcid":"https://orcid.org/0000-0001-8911-8977"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Lins Denaux","raw_affiliation_strings":["Department of Mathematics: Analysis Logic and Discrete Mathematics, Ghent University, Ghent, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-8911-8977","affiliations":[{"raw_affiliation_string":"Department of Mathematics: Analysis Logic and Discrete Mathematics, Ghent University, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061433215","display_name":"Leo Storme","orcid":"https://orcid.org/0000-0001-6440-9225"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Leo Storme","raw_affiliation_strings":["Department of Mathematics: Analysis Logic and Discrete Mathematics, Ghent University, Ghent, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-6440-9225","affiliations":[{"raw_affiliation_string":"Department of Mathematics: Analysis Logic and Discrete Mathematics, Ghent University, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064007468","display_name":"Zsuzsa Weiner","orcid":null},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Zsuzsa Weiner","raw_affiliation_strings":["MTA\u2014ELTE Geometric and Algebraic Combinatorics Research Group, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MTA\u2014ELTE Geometric and Algebraic Combinatorics Research Group, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00554121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9984999895095825,"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":0.9984999895095825,"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/T10849","display_name":"Finite Group Theory Research","score":0.9952999949455261,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9491999745368958,"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/hyperplane","display_name":"Hyperplane","score":0.9643003940582275},{"id":"https://openalex.org/keywords/incidence","display_name":"Incidence (geometry)","score":0.7520437240600586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.685104250907898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6724045872688293},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6163932085037231},{"id":"https://openalex.org/keywords/projective-space","display_name":"Projective space","score":0.4645163118839264},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4497041404247284},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42481300234794617},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.413418173789978},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.16821932792663574},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1317490041255951},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12624230980873108},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.09695282578468323},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08788943290710449}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.9643003940582275},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.7520437240600586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.685104250907898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6724045872688293},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6163932085037231},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.4645163118839264},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4497041404247284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42481300234794617},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.413418173789978},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.16821932792663574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1317490041255951},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12624230980873108},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.09695282578468323},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08788943290710449},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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":4,"locations":[{"id":"pmh:oai:vubissmart:VUBISSMART:2000:127519","is_oa":false,"landing_page_url":"https://biblio.vub.ac.be/vubir/small-weight-code-words-arising-from-the-incidence-of-points-and-hyperplanes-in-pgnq(17d494df-732b-44b5-9853-624377cf02cb).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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:vubissmart:VUBISSMART:2000:127519","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-019-00710-0","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:archive.ugent.be:8641545","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-8641545","pdf_url":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1573-7586","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"mag:3021830697","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2417812136","https://openalex.org/W2579583995","https://openalex.org/W2780505258","https://openalex.org/W2678492110","https://openalex.org/W2951559513","https://openalex.org/W2993107159","https://openalex.org/W2065264478","https://openalex.org/W2156184439","https://openalex.org/W3105624231","https://openalex.org/W2963265845","https://openalex.org/W2962848459","https://openalex.org/W2024729953","https://openalex.org/W2321181239","https://openalex.org/W2741168160","https://openalex.org/W2486121825","https://openalex.org/W2332801594","https://openalex.org/W1988680385","https://openalex.org/W2728921436","https://openalex.org/W1970529671","https://openalex.org/W2088372202"],"abstract_inverted_index":{"Let":[0],"Cn\u22121(n,q)":[1],"be":[2],"the":[3,7,14,49,56,59],"code":[4,37,70],"arising":[5],"from":[6],"incidence":[8,50,60,81],"of":[9,39,47,52,58,62,72,80,83,96],"points":[10],"and":[11,21],"hyperplanes":[12,84],"in":[13],"Desarguesian":[15],"projective":[16],"space":[17],"PG(n,q).":[18],"Recently,":[19],"Polverino":[20],"Zullo":[22],"(J":[23],"Comb":[24],"Theory":[25],"Ser":[26],"A":[27],"158:1\u201311,":[28],"2018)":[29],"proved":[30],"that":[31,68],"within":[32],"this":[33],"code,":[34],"all":[35,69],"non-zero":[36],"words":[38,71],"weight":[40,73],"at":[41,74],"most":[42,75],"2qn\u22121":[43],"are":[44,77],"scalar":[45],"multiples":[46],"either":[48],"vector":[51],"one":[53],"hyperplane,":[54],"or":[55],"difference":[57],"vectors":[61,82],"two":[63],"distinct":[64],"hyperplanes.":[65],"We":[66],"prove":[67],"(4q\u2212O(q\u221a))qn\u22122":[76],"linear":[78],"combinations":[79],"through":[85],"a":[86],"common":[87],"(n\u22123)-space.":[88],"This":[89],"extends":[90],"previous":[91],"results":[92],"for":[93],"large":[94],"values":[95],"q.":[97]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}