{"id":"https://openalex.org/W2588833479","doi":"https://doi.org/10.3934/amc.2017011","title":"Codes from hall planes of odd order","display_name":"Codes from hall planes of odd order","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2588833479","doi":"https://doi.org/10.3934/amc.2017011","mag":"2588833479"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2017011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017011","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2017011","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030001589","display_name":"J. D. Key","orcid":"https://orcid.org/0000-0002-1487-8127"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. D. Key","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000911611","display_name":"T. P. McDonough","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. P. McDonough","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111481610","display_name":"V. C. Mavron","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. C. Mavron","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030001589"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01396844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"1","first_page":"179","last_page":"185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.814244270324707},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7390032410621643},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.7365062832832336},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.7291632294654846},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.7117980718612671},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6698375940322876},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.6694110035896301},{"id":"https://openalex.org/keywords/ternary-golay-code","display_name":"Ternary Golay code","score":0.5189842581748962},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4911770522594452},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44758903980255127},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.41904211044311523},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37751513719558716},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27515408396720886},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.12959372997283936},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11146363615989685},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.08418792486190796},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07761773467063904},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.0746569037437439},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05238741636276245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.814244270324707},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7390032410621643},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.7365062832832336},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.7291632294654846},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.7117980718612671},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6698375940322876},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.6694110035896301},{"id":"https://openalex.org/C108906091","wikidata":"https://www.wikidata.org/wiki/Q7702927","display_name":"Ternary Golay code","level":5,"score":0.5189842581748962},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4911770522594452},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44758903980255127},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.41904211044311523},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37751513719558716},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27515408396720886},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.12959372997283936},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11146363615989685},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.08418792486190796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07761773467063904},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0746569037437439},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05238741636276245},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2017011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017011","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2017011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017011","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W575638596","https://openalex.org/W1976677460","https://openalex.org/W2030589010","https://openalex.org/W2034493900","https://openalex.org/W2092672993","https://openalex.org/W2129121973","https://openalex.org/W2182596671","https://openalex.org/W2912810145","https://openalex.org/W4211147273","https://openalex.org/W6759307017"],"related_works":["https://openalex.org/W2093452027","https://openalex.org/W1995177878","https://openalex.org/W2014783995","https://openalex.org/W1989082250","https://openalex.org/W2070443794","https://openalex.org/W2165464723","https://openalex.org/W1986433874","https://openalex.org/W3189288785","https://openalex.org/W2120879624","https://openalex.org/W2588833479"],"abstract_inverted_index":{"We":[0],"show":[1],"explicitly":[2],"that":[3,64,75],"the":[4,7,11,20,23,27,44,49,67,71,77],"dimension":[5,21],"of":[6,10,14,22,26,30,48,52,70],"ternary":[8,24,46],"code":[9,25,47,69],"Hall":[12],"plane":[13,29,51,74],"order":[15,31,53],"9":[16],"is":[17],"greater":[18],"than":[19],"desarguesian":[28,50,72],"9.":[32,54],"The":[33,55],"proof":[34],"requires":[35],"finding":[36],"a":[37],"word":[38],"with":[39],"some":[40],"defined":[41],"properties":[42,79],"in":[43,66],"dual":[45,68],"idea":[56],"can":[57,80],"be":[58,81],"generalised":[59],"for":[60],"other":[61],"orders,":[62],"provided":[63],"words":[65],"projective":[73],"have":[76],"specified":[78],"found.":[82]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
