{"id":"https://openalex.org/W2761107935","doi":"https://doi.org/10.1109/tit.2012.2196255","title":"On the Classification of Hermitian Self-Dual Additive Codes Over ${\\rm GF}(9)$","display_name":"On the Classification of Hermitian Self-Dual Additive Codes Over ${\\rm GF}(9)$","publication_year":2012,"publication_date":"2012-04-27","ids":{"openalex":"https://openalex.org/W2761107935","doi":"https://doi.org/10.1109/tit.2012.2196255","mag":"2761107935"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2196255","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2196255","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":null,"display_name":"Lars Eirik Danielsen","orcid":null},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Lars Eirik Danielsen","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":null,"apc_paid":null,"fwci":3.1133,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.92412321,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"8","first_page":"5500","last_page":"5511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987999796867371,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9977999925613403,"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/block-code","display_name":"Block code","score":0.6237999796867371},{"id":"https://openalex.org/keywords/expander-code","display_name":"Expander code","score":0.5647000074386597},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5375000238418579},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5299999713897705},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.4172999858856201},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.4147999882698059},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.4088999927043915},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.40720000863075256},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.37229999899864197},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.3547999858856201}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.694100022315979},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.6237999796867371},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5724999904632568},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.5647000074386597},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5375000238418579},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5299999713897705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4397999942302704},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.4172999858856201},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.4147999882698059},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.4088999927043915},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.40720000863075256},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.34119999408721924},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.3336000144481659},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.328000009059906},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.32519999146461487},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C76132124","wikidata":"https://www.wikidata.org/wiki/Q5474786","display_name":"Fountain code","level":5,"score":0.30230000615119934},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.29100000858306885},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.2897000014781952},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C69497775","wikidata":"https://www.wikidata.org/wiki/Q7269025","display_name":"Quantum convolutional code","level":5,"score":0.2851000130176544},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C56654003","wikidata":"https://www.wikidata.org/wiki/Q7858715","display_name":"Two-graph","level":5,"score":0.26989999413490295},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26420000195503235},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.2621000111103058},{"id":"https://openalex.org/C20079647","wikidata":"https://www.wikidata.org/wiki/Q1278039","display_name":"Prefix code","level":5,"score":0.26010000705718994},{"id":"https://openalex.org/C108906091","wikidata":"https://www.wikidata.org/wiki/Q7702927","display_name":"Ternary Golay code","level":5,"score":0.2515000104904175},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.25119999051094055},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2012.2196255","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2196255","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W421958857","https://openalex.org/W1606879738","https://openalex.org/W1964589141","https://openalex.org/W1996530820","https://openalex.org/W2007652806","https://openalex.org/W2018745606","https://openalex.org/W2040415704","https://openalex.org/W2074394986","https://openalex.org/W2075359144","https://openalex.org/W2103981000","https://openalex.org/W2107407019","https://openalex.org/W2111381006","https://openalex.org/W2114436764","https://openalex.org/W2117356938","https://openalex.org/W2123849728","https://openalex.org/W2128751442","https://openalex.org/W2141424941","https://openalex.org/W2152039952","https://openalex.org/W2162938940","https://openalex.org/W2164713002","https://openalex.org/W2165148883","https://openalex.org/W2167413626","https://openalex.org/W2608977424","https://openalex.org/W4206433460","https://openalex.org/W6638655328"],"related_works":[],"abstract_inverted_index":{"Additive":[0],"codes":[1,33,47,58,78,152,170,186],"over":[2,48,59],"GF(9)":[3,60],"that":[4,93,111,128],"are":[5,146,159],"self-dual":[6,45,99],"with":[7,187],"respect":[8],"to":[9,26,52,65,77,117,148],"the":[10,74,109,130,184],"Hermitian":[11],"trace":[12],"inner":[13],"product":[14],"have":[15,34,61],"a":[16,90,118,122,136],"natural":[17],"application":[18],"in":[19,69],"quantum":[20,28,54],"information":[21],"theory,":[22],"where":[23],"they":[24],"correspond":[25,51],"ternary":[27],"error-correcting":[29],"codes.":[30,55,101,180],"However,":[31],"these":[32],"so":[35],"far":[36,38],"received":[37],"less":[39],"interest":[40],"from":[41],"coding":[42],"theorists":[43],"than":[44],"additive":[46,57,100],"GF(4),":[49],"which":[50],"binary":[53],"Self-dual":[56],"been":[62],"classified":[63],"up":[64],"length":[66],"8,":[67],"and":[68,82,121,156,171],"this":[70],"paper":[71],"we":[72,145],"extend":[73],"complete":[75],"classification":[76,85],"of":[79,98,132,138,153],"lengths":[80,154],"9":[81],"10.":[83],"The":[84,102],"is":[86,105,125],"obtained":[87],"by":[88,108],"using":[89],"new":[91],"algorithm":[92],"combines":[94],"two":[95],"graph":[96,124,139],"representations":[97],"search":[103],"space":[104],"first":[106],"reduced":[107],"fact":[110],"every":[112],"code":[113,133],"can":[114],"be":[115],"mapped":[116],"weighted":[119],"graph,":[120],"different":[123],"then":[126],"introduced":[127],"transforms":[129],"problem":[131,137],"equivalence":[134],"into":[135],"isomorphism.":[140],"By":[141],"an":[142],"extension":[143],"technique,":[144],"able":[147],"classify":[149],"all":[150],"optimal":[151],"11":[155],"12.":[157],"There":[158],"56":[160],"005":[161],"876":[162],"(11,":[163],"3":[164,174],"<sup":[165,175],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[166,176],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">11</sup>":[167],",":[168,178],"5)":[169],"6493":[172],"(12,":[173],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">12</sup>":[177],"6)":[179],"We":[181],"also":[182],"find":[183],"smallest":[185],"trivial":[188],"automorphism":[189],"group.":[190]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2017-10-20T00:00:00"}
