{"id":"https://openalex.org/W2107176733","doi":"https://doi.org/10.1007/s10623-012-9667-5","title":"The generating rank of the space of short vectors in the Leech lattice mod 2","display_name":"The generating rank of the space of short vectors in the Leech lattice mod 2","publication_year":2012,"publication_date":"2012-04-08","ids":{"openalex":"https://openalex.org/W2107176733","doi":"https://doi.org/10.1007/s10623-012-9667-5","mag":"2107176733"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-012-9667-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-012-9667-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-012-9667-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-012-9667-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105369849","display_name":"Andries E. Brouwer","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Andries Brouwer","raw_affiliation_strings":["Department of Mathematics, Technical University Eindhoven, P.O. Box 513, 5600\u00a0MB, Eindhoven, The Netherlands","Department of Mathematics, Technical University Eindhoven, Eindhoven, The Netherlands 5600 MB#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University Eindhoven, P.O. Box 513, 5600\u00a0MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Department of Mathematics, Technical University Eindhoven, Eindhoven, The Netherlands 5600 MB#TAB#","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082493210","display_name":"\u00c7\u00ed\u00e7ek G\u00fcven","orcid":"https://orcid.org/0000-0002-1939-8325"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"\u00c7i\u00e7ek G\u00fcven","raw_affiliation_strings":["Department of Mathematics, Technical University Eindhoven, P.O. Box 513, 5600\u00a0MB, Eindhoven, The Netherlands","Department of Mathematics, Technical University Eindhoven, Eindhoven, The Netherlands 5600 MB#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University Eindhoven, P.O. Box 513, 5600\u00a0MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Department of Mathematics, Technical University Eindhoven, Eindhoven, The Netherlands 5600 MB#TAB#","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12910444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"1-2","first_page":"107","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9987000226974487,"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/T11797","display_name":"graph theory and CDMA systems","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.7936662435531616},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6032159924507141},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6022984981536865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5956808924674988},{"id":"https://openalex.org/keywords/leech","display_name":"Leech","score":0.5288083553314209},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4977834224700928},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.48014017939567566},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4505902826786041},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.4463486075401306},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.41226738691329956},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36637410521507263},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3208928108215332},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25131916999816895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19702783226966858},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12443092465400696}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7936662435531616},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6032159924507141},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6022984981536865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5956808924674988},{"id":"https://openalex.org/C180746962","wikidata":"https://www.wikidata.org/wiki/Q243147","display_name":"Leech","level":2,"score":0.5288083553314209},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4977834224700928},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.48014017939567566},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4505902826786041},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.4463486075401306},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.41226738691329956},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36637410521507263},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3208928108215332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25131916999816895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19702783226966858},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12443092465400696},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10623-012-9667-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-012-9667-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-012-9667-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire/7f5581de-f619-4390-a53e-9b8fe55f8021","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/7f5581de-f619-4390-a53e-9b8fe55f8021","pdf_url":"https://research.tue.nl/files/3553753/620479017671030.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Brouwer, A E & G\u00fcven, \u00c7 2012, 'The generating rank of the space of short vectors in the Leech lattice mod 2', Designs, Codes and Cryptography, vol. 65, no. 1-2, pp. 107-113. https://doi.org/10.1007/s10623-012-9667-5","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:733327","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=733327","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0925-1022","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:733327","is_oa":false,"landing_page_url":"http://repository.tue.nl/733327","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0925-1022","raw_type":"Article / Letter to the editor"},{"id":"pmh:tue:oai:pure.tue.nl:publications/7f5581de-f619-4390-a53e-9b8fe55f8021","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/7f5581de-f619-4390-a53e-9b8fe55f8021","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, Codes and Cryptography, 65(1-2), 107 - 113. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10623-012-9667-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-012-9667-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-012-9667-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2107176733.pdf","grobid_xml":"https://content.openalex.org/works/W2107176733.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1995990042","https://openalex.org/W2044656335","https://openalex.org/W2118251972","https://openalex.org/W4293259454"],"related_works":["https://openalex.org/W2143240605","https://openalex.org/W2380131535","https://openalex.org/W4381683346","https://openalex.org/W2409527406","https://openalex.org/W2891310375","https://openalex.org/W2365675088","https://openalex.org/W119127995","https://openalex.org/W2016852223","https://openalex.org/W2351168130","https://openalex.org/W2015540166"],"abstract_inverted_index":{"Consider":[0],"the":[1,6,11,16,21,24,34,39],"partial":[2],"linear":[3],"space":[4,44],"on":[5],"images":[7],"in":[8,15],"\u039b/2\u039b":[9],"of":[10,26,42],"shortest":[12],"nonzero":[13],"vectors":[14,27],"Leech":[17],"lattice":[18],"\u039b,":[19],"where":[20],"lines":[22],"are":[23,46],"triples":[25],"adding":[28],"up":[29],"to":[30],"zero.":[31],"We":[32],"determine":[33],"universal":[35],"embedding":[36],"dimension":[37],"and":[38,48],"generating":[40],"rank":[41],"this":[43],"(both":[45],"24)":[47],"classify":[49],"its":[50],"hyperplanes.":[51]},"counts_by_year":[],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}