{"id":"https://openalex.org/W2016256153","doi":"https://doi.org/10.1109/isit.2014.6875249","title":"Constructions a of lattices from number fields and division algebras","display_name":"Constructions a of lattices from number fields and division algebras","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2016256153","doi":"https://doi.org/10.1109/isit.2014.6875249","mag":"2016256153"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2014.6875249","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2014.6875249","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dr.ntu.edu.sg/bitstream/10356/79610/1/isitrwf_v5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034251584","display_name":"Roope Vehkalahti","orcid":"https://orcid.org/0000-0002-3052-0635"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Roope Vehkalahti","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Turku, Finland","Dept. of Math. & Stat., Univ. of Turku, Turku, , Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Turku, Finland","institution_ids":["https://openalex.org/I155660961"]},{"raw_affiliation_string":"Dept. of Math. & Stat., Univ. of Turku, Turku, , Finland","institution_ids":["https://openalex.org/I155660961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001009310","display_name":"Wittawat Kositwattanarerk","orcid":null},"institutions":[{"id":"https://openalex.org/I25399158","display_name":"Mahidol University","ror":"https://ror.org/01znkr924","country_code":"TH","type":"education","lineage":["https://openalex.org/I25399158"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Wittawat Kositwattanarerk","raw_affiliation_strings":["Department of Mathematics, Mahidol University, Bangkok, Thailand","Dept. of Math., Mahidol Univ., Bangkok, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mahidol University, Bangkok, Thailand","institution_ids":["https://openalex.org/I25399158"]},{"raw_affiliation_string":"Dept. of Math., Mahidol Univ., Bangkok, Thailand","institution_ids":["https://openalex.org/I25399158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031189447","display_name":"Fr\u00e9d\u00e9rique Oggier","orcid":"https://orcid.org/0000-0003-3141-3118"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Frederique Oggier","raw_affiliation_strings":["Division of Mathematical Sciences, Nanyang Technological University, Singapore","Div. of Math. Sci., Nanyang Technol. Univ., Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Div. of Math. Sci., Nanyang Technol. Univ., Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034251584"],"corresponding_institution_ids":["https://openalex.org/I155660961"],"apc_list":null,"apc_paid":null,"fwci":0.8457,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80886106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"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":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9990000128746033,"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/hamming-distance","display_name":"Hamming distance","score":0.7145171165466309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5979412794113159},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.5833711624145508},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.567297637462616},{"id":"https://openalex.org/keywords/gaussian-binomial-coefficient","display_name":"Gaussian binomial coefficient","score":0.5643360018730164},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5334881544113159},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5215204358100891},{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.4900745153427124},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.48695263266563416},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4695105254650116},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4105123281478882},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3771815001964569},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3433120846748352},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.17747706174850464},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16836485266685486},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10440889000892639},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08283519744873047}],"concepts":[{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.7145171165466309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5979412794113159},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.5833711624145508},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.567297637462616},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.5643360018730164},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5334881544113159},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5215204358100891},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.4900745153427124},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.48695263266563416},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4695105254650116},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4105123281478882},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3771815001964569},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3433120846748352},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.17747706174850464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16836485266685486},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10440889000892639},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08283519744873047},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2014.6875249","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2014.6875249","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/79610","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/20940","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/79610/1/isitrwf_v5.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Conference Paper"}],"best_oa_location":{"id":"pmh:oai:dr.ntu.edu.sg:10356/79610","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/20940","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/79610/1/isitrwf_v5.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Conference Paper"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3034753964","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G3417082185","display_name":null,"funder_award_id":"NRF-RF2009-07","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320709","display_name":"National Research Foundation Singapore","ror":"https://ror.org/03cpyc314"},{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"},{"id":"https://openalex.org/F4320323313","display_name":"Turun Yliopisto","ror":"https://ror.org/05vghhr25"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2016256153.pdf","grobid_xml":"https://content.openalex.org/works/W2016256153.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1560609861","https://openalex.org/W2098217413","https://openalex.org/W2110962034","https://openalex.org/W2125233053","https://openalex.org/W2131764879","https://openalex.org/W2158143594","https://openalex.org/W2332123861","https://openalex.org/W2914786679","https://openalex.org/W6678446630"],"related_works":["https://openalex.org/W2105471374","https://openalex.org/W2740543340","https://openalex.org/W2008960744","https://openalex.org/W2067417168","https://openalex.org/W4283763810","https://openalex.org/W1519122282","https://openalex.org/W2098310607","https://openalex.org/W153182557","https://openalex.org/W1582340598","https://openalex.org/W2779867339"],"abstract_inverted_index":{"There":[0],"is":[1,37,102,113],"a":[2,62],"rich":[3],"theory":[4,17],"of":[5,35,46,54,74,91,98,108],"relations":[6],"between":[7],"lattices":[8],"and":[9,118],"linear":[10,48],"codes":[11,24,101],"over":[12],"finite":[13,100],"fields.":[14],"However,":[15],"this":[16],"has":[18],"been":[19],"developed":[20],"mostly":[21],"with":[22],"lattice":[23],"for":[25,66],"the":[26,43,47,51,55,92,95,99,105,109,114,119],"Gaussian":[27],"channel":[28,68],"in":[29],"mind.":[30],"In":[31],"particular,":[32],"different":[33],"versions":[34,73],"what":[36],"called":[38],"Construction":[39,75],"A":[40,76],"have":[41],"connected":[42,103],"Hamming":[44,96],"distance":[45,97,107,117],"code":[49],"to":[50,86,104],"Euclidean":[52,93],"structure":[53],"lattice.":[56],"This":[57],"paper":[58],"concentrates":[59],"on":[60],"developing":[61],"similar":[63],"theory,":[64],"but":[65],"fading":[67],"coding":[69],"instead.":[70],"First,":[71],"two":[72],"from":[77],"number":[78],"fields":[79],"are":[80,83],"given.":[81],"These":[82],"then":[84],"extended":[85],"division":[87],"algebra":[88],"lattices.":[89],"Instead":[90],"distance,":[94],"product":[106,116],"resulting":[110],"lattices,":[111],"that":[112],"minimum":[115,120],"determinant":[121],"respectively.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}