{"id":"https://openalex.org/W2057277076","doi":"https://doi.org/10.1007/s10623-010-9469-6","title":"Directed graph representation of half-rate additive codes over GF(4)","display_name":"Directed graph representation of half-rate additive codes over GF(4)","publication_year":2010,"publication_date":"2010-12-07","ids":{"openalex":"https://openalex.org/W2057277076","doi":"https://doi.org/10.1007/s10623-010-9469-6","mag":"2057277076"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-010-9469-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-010-9469-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-010-9469-6.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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-010-9469-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078793078","display_name":"Lars Eirik Danielsen","orcid":"https://orcid.org/0000-0002-5141-0531"},"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, PO Box 7803, 5020, Bergen, Norway","Department of informatics, University of Bergen, Bergen, Norway 5020#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, PO Box 7803, 5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Department of informatics, University of Bergen, Bergen, Norway 5020#TAB#","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061571294","display_name":"Matthew G. Parker","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":false,"raw_author_name":"Matthew G. Parker","raw_affiliation_strings":["Department of Informatics, University of Bergen, PO Box 7803, 5020, Bergen, Norway","Department of informatics, University of Bergen, Bergen, Norway 5020#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, PO Box 7803, 5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Department of informatics, University of Bergen, Bergen, Norway 5020#TAB#","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078793078"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.9327,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8094223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"59","issue":"1-3","first_page":"119","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","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/T11130","display_name":"Coding theory and cryptography","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/T11321","display_name":"Error Correcting Code Techniques","score":0.9943000078201294,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9937999844551086,"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/circulant-matrix","display_name":"Circulant matrix","score":0.7230870723724365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5997791290283203},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.567362904548645},{"id":"https://openalex.org/keywords/expander-code","display_name":"Expander code","score":0.5288302302360535},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5080375671386719},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4541487395763397},{"id":"https://openalex.org/keywords/circulant-graph","display_name":"Circulant graph","score":0.4512750208377838},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4478170871734619},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.42401039600372314},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4179779887199402},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.4104453921318054},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3798734247684479},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27912139892578125},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.18802443146705627},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18200761079788208},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.12296891212463379},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.07787683606147766}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.7230870723724365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5997791290283203},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.567362904548645},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.5288302302360535},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5080375671386719},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4541487395763397},{"id":"https://openalex.org/C82190004","wikidata":"https://www.wikidata.org/wiki/Q5121633","display_name":"Circulant graph","level":5,"score":0.4512750208377838},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4478170871734619},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.42401039600372314},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4179779887199402},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.4104453921318054},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3798734247684479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27912139892578125},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.18802443146705627},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18200761079788208},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.12296891212463379},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.07787683606147766},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/s10623-010-9469-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-010-9469-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-010-9469-6.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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0902.3883","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0902.3883","pdf_url":"https://arxiv.org/pdf/0902.3883","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.7483","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.7483","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ii.uib.no/~matthew/DirectedGraph.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.8144","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.8144","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ii.uib.no/~larsed/directed.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.7221","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.7221","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ii.uib.no/~larsed/directed.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.248.112","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.112","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0902.3883v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.248.2787","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.2787","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0902.3883v2.pdf","raw_type":"text"},{"id":"pmh:oai:bora.uib.no:1956/4550","is_oa":true,"landing_page_url":"http://hdl.handle.net/1956/4550","pdf_url":null,"source":{"id":"https://openalex.org/S4306400085","display_name":"Bergen Open Research Archive (BORA) (University of Bergen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4432739","host_organization_name":"University of Bergen","host_organization_lineage":["https://openalex.org/I4432739"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/other"}],"best_oa_location":{"id":"doi:10.1007/s10623-010-9469-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-010-9469-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-010-9469-6.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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2057277076.pdf","grobid_xml":"https://content.openalex.org/works/W2057277076.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1503834475","https://openalex.org/W1516318957","https://openalex.org/W1556443961","https://openalex.org/W1570550740","https://openalex.org/W1606879738","https://openalex.org/W1617868970","https://openalex.org/W1964589141","https://openalex.org/W2037033741","https://openalex.org/W2056498695","https://openalex.org/W2062984219","https://openalex.org/W2089947878","https://openalex.org/W2097151077","https://openalex.org/W2108515345","https://openalex.org/W2114436764","https://openalex.org/W2118909434","https://openalex.org/W2123849728","https://openalex.org/W2126209209","https://openalex.org/W2126870031","https://openalex.org/W2141424941","https://openalex.org/W2164713002","https://openalex.org/W2165148883","https://openalex.org/W2167413626","https://openalex.org/W2572379384","https://openalex.org/W2608977424","https://openalex.org/W3105797017"],"related_works":["https://openalex.org/W2293846540","https://openalex.org/W1976052006","https://openalex.org/W3021758908","https://openalex.org/W1998728561","https://openalex.org/W4386066307","https://openalex.org/W3045580795","https://openalex.org/W2095450438","https://openalex.org/W2098505542","https://openalex.org/W4248142543","https://openalex.org/W2041319252"],"abstract_inverted_index":{"We":[0,70],"show":[1,83],"that":[2,84,104],"(n,":[3,46],"2":[4,47],"n":[5,48],")":[6,49],"additive":[7,23,45],"codes":[8,24,50,86,97,109,122,130],"over":[9,25,51],"GF(4)":[10,52],"can":[11],"be":[12,89],"represented":[13],"as":[14],"directed":[15,79],"graphs.":[16,31],"This":[17],"generalizes":[18],"earlier":[19],"results":[20],"on":[21],"self-dual":[22,68,121,145],"GF(4),":[26],"which":[27],"correspond":[28],"to":[29,43,56,101],"undirected":[30],"Graph":[32],"representation":[33],"reduces":[34],"the":[35,142],"complexity":[36],"of":[37,53,64,74,94,98,110,123,131],"code":[38],"classification,":[39],"and":[40,66,76,82,126,128,135],"enables":[41],"us":[42],"classify":[44],"length":[54,99,124,132],"up":[55,100],"7.":[57],"From":[58],"this":[59],"we":[60,116],"also":[61],"derive":[62],"classifications":[63],"isodual":[65,129],"formally":[67,120],"codes.":[69,146],"introduce":[71],"new":[72,118],"constructions":[73,106],"circulant":[75,78],"bordered":[77],"graph":[80],"codes,":[81],"these":[85,105],"will":[87],"always":[88],"isodual.":[90],"A":[91],"computer":[92],"search":[93],"all":[95],"such":[96],"26":[102,136],"reveals":[103],"produce":[107],"many":[108],"high":[111],"minimum":[112,139],"distance.":[113],"In":[114],"particular,":[115],"find":[117],"near-extremal":[119],"11":[125],"13,":[127],"24,":[133],"25,":[134],"with":[137],"better":[138],"distance":[140],"than":[141],"best":[143],"known":[144]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
