{"id":"https://openalex.org/W2518503017","doi":"https://doi.org/10.3934/amc.2016027","title":"There is no $[24,12,9]$ doubly-even self-dual code over $\\mathbb F_4$","display_name":"There is no $[24,12,9]$ doubly-even self-dual code over $\\mathbb F_4$","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2518503017","doi":"https://doi.org/10.3934/amc.2016027","mag":"2518503017"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2016027","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016027","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=618fdc6a-afe8-4394-94fc-e32aa0c47f1e","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://www.aimsciences.org/article/exportPdf?id=618fdc6a-afe8-4394-94fc-e32aa0c47f1e","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007240524","display_name":"Sihuang Hu","orcid":"https://orcid.org/0000-0002-2910-3025"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sihuang Hu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029375442","display_name":"Gabriele Nebe","orcid":"https://orcid.org/0000-0002-5297-5542"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabriele Nebe","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007240524"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05788553,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"3","first_page":"583","last_page":"588"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9915000200271606,"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/T12162","display_name":"Cellular Automata and Applications","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8826462030410767},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.7387312650680542},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6633254885673523},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5485506653785706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3530580401420593},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06308463215827942},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.061828047037124634},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.048592180013656616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8826462030410767},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.7387312650680542},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6633254885673523},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5485506653785706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3530580401420593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06308463215827942},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.061828047037124634},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.048592180013656616},{"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.2016027","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016027","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=618fdc6a-afe8-4394-94fc-e32aa0c47f1e","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.2016027","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016027","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=618fdc6a-afe8-4394-94fc-e32aa0c47f1e","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2518503017.pdf","grobid_xml":"https://content.openalex.org/works/W2518503017.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1559343931","https://openalex.org/W1976677460","https://openalex.org/W2015337464","https://openalex.org/W2037078554","https://openalex.org/W2052221455","https://openalex.org/W2056477520","https://openalex.org/W2071993485","https://openalex.org/W2095701235","https://openalex.org/W4206775542"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"there":[3],"is":[4],"no":[5],"$[24,12,9]$":[6],"doubly-even":[7],"self-dual":[8],"code":[9,21],"over":[10],"$\\mathbb{F}_4$":[11],"by":[12],"attempting":[13],"to":[14],"construct":[15],"the":[16],"generator":[17],"matrix":[18],"of":[19],"this":[20],"directly.":[22]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}