{"id":"https://openalex.org/W2121052240","doi":"https://doi.org/10.1109/tit.2010.2080571","title":"Reflection Group Codes and Their Decoding","display_name":"Reflection Group Codes and Their Decoding","publication_year":2010,"publication_date":"2010-11-30","ids":{"openalex":"https://openalex.org/W2121052240","doi":"https://doi.org/10.1109/tit.2010.2080571","mag":"2121052240"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2080571","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2080571","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5105718844","display_name":"William Wesley Peterson","orcid":null},"institutions":[{"id":"https://openalex.org/I1331384533","display_name":"University of Hawaii System","ror":"https://ror.org/03tzaeb71","country_code":"US","type":"education","lineage":["https://openalex.org/I1331384533"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. Wesley Peterson","raw_affiliation_strings":["Department of ICS, University of Hawai, Honolulu, HI, USA","Dept. of ICS, Univ. of Hawaii, Honolulu, HI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ICS, University of Hawai, Honolulu, HI, USA","institution_ids":["https://openalex.org/I1331384533"]},{"raw_affiliation_string":"Dept. of ICS, Univ. of Hawaii, Honolulu, HI, USA","institution_ids":["https://openalex.org/I1331384533"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057623811","display_name":"J. B. Nation","orcid":"https://orcid.org/0000-0001-5959-3304"},"institutions":[{"id":"https://openalex.org/I1331384533","display_name":"University of Hawaii System","ror":"https://ror.org/03tzaeb71","country_code":"US","type":"education","lineage":["https://openalex.org/I1331384533"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. B. Nation","raw_affiliation_strings":["Department of Mathematics, University of Hawaii, Honolulu, HI, USA","Dept. of Math., Univ. of Hawaii, Honolulu, HI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hawaii, Honolulu, HI, USA","institution_ids":["https://openalex.org/I1331384533"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Hawaii, Honolulu, HI, USA","institution_ids":["https://openalex.org/I1331384533"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059876548","display_name":"M.P.C. Fossorier","orcid":"https://orcid.org/0000-0002-3646-2050"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]},{"id":"https://openalex.org/I4210148552","display_name":"Equipes Traitement de l'Information et Syst\u00e8mes","ror":"https://ror.org/0592ata02","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210142324","https://openalex.org/I4210148552","https://openalex.org/I4210159245","https://openalex.org/I86175216"]},{"id":"https://openalex.org/I86175216","display_name":"\u00c9cole Nationale Sup\u00e9rieure de l'\u00c9lectronique et de ses Applications","ror":"https://ror.org/03qeacd72","country_code":"FR","type":"education","lineage":["https://openalex.org/I86175216"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc P. Fossorier","raw_affiliation_strings":["ETIS, ENSEA/UCP/CNRS, Cergy-Pontoise, France","ETIS ENSEA, UCP, Cergy -Pontoise, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETIS, ENSEA/UCP/CNRS, Cergy-Pontoise, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210142324","https://openalex.org/I4210148552","https://openalex.org/I86175216"]},{"raw_affiliation_string":"ETIS ENSEA, UCP, Cergy -Pontoise, France","institution_ids":["https://openalex.org/I4210142324","https://openalex.org/I86175216"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0239,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.88734135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"12","first_page":"6273","last_page":"6293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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":0.996399998664856,"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/decoding-methods","display_name":"Decoding methods","score":0.8975001573562622},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.7714126110076904},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.7359268069267273},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.6038239002227783},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5599777102470398},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.5551354289054871},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4950191378593445},{"id":"https://openalex.org/keywords/berlekamp\u2013welch-algorithm","display_name":"Berlekamp\u2013Welch algorithm","score":0.4824402928352356},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4505385756492615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38938623666763306},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37323421239852905},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.25503113865852356},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1723499894142151},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.14041322469711304}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.8975001573562622},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.7714126110076904},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.7359268069267273},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.6038239002227783},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5599777102470398},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.5551354289054871},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4950191378593445},{"id":"https://openalex.org/C132727834","wikidata":"https://www.wikidata.org/wiki/Q4892328","display_name":"Berlekamp\u2013Welch algorithm","level":5,"score":0.4824402928352356},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4505385756492615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38938623666763306},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37323421239852905},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.25503113865852356},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1723499894142151},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.14041322469711304},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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":5,"locations":[{"id":"doi:10.1109/tit.2010.2080571","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2080571","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.159.8881","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.8881","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hawaii.edu/~jb/ieee720.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.170.6565","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.6565","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hawaii.edu/%7Ejb/ieee7710.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.174.8961","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.8961","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hawaii.edu/%7Ejb/IEEEpageproofsfinal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.216.859","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.216.859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hawaii.edu/~jb/ieee720.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W169388539","https://openalex.org/W1975170301","https://openalex.org/W1979598217","https://openalex.org/W2009190506","https://openalex.org/W2025829207","https://openalex.org/W2046273783","https://openalex.org/W2080982356","https://openalex.org/W2120316028","https://openalex.org/W2155904881","https://openalex.org/W2166905766","https://openalex.org/W2293169577","https://openalex.org/W2572527475","https://openalex.org/W3198160809","https://openalex.org/W4210801347","https://openalex.org/W4213459181","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2385322349","https://openalex.org/W2369600518","https://openalex.org/W2370284973","https://openalex.org/W2357077655","https://openalex.org/W2351361564","https://openalex.org/W2144831582","https://openalex.org/W2129423808","https://openalex.org/W4205451769","https://openalex.org/W1976480044","https://openalex.org/W2029144766"],"abstract_inverted_index":{"This":[0],"paper":[1],"builds":[2],"on":[3,16,29],"Mittelholzer":[4],"and":[5,41,59],"Lahtonen's":[6],"study":[7],"of":[8,22,25,36,55,67,70,83],"group":[9,28],"codes":[10],"for":[11,39],"the":[12,23,34,68,74,81],"Gaussian":[13],"channel":[14],"based":[15],"reflection":[17,27],"groups.":[18],"A":[19],"careful":[20],"analysis":[21],"action":[24],"a":[26,64],"its":[30],"roots":[31],"leads":[32],"to":[33,48],"development":[35],"improved":[37],"methods":[38],"encoding":[40],"decoding.":[42,52,84],"The":[43,53],"new":[44],"algorithm":[45,75],"is":[46,57,61],"proved":[47],"achieve":[49],"maximum":[50],"likelihood":[51],"complexity":[54],"decoding":[56],"analyzed,":[58],"it":[60],"shown":[62],"that":[63],"proper":[65],"choice":[66],"sequence":[69],"subgroups":[71],"used":[72],"in":[73,80],"can":[76],"yield":[77],"significant":[78],"gains":[79],"efficiency":[82]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
