{"id":"https://openalex.org/W2270827087","doi":"https://doi.org/10.1109/tit.2017.2654456","title":"Generalized Hamming Weights for Almost Affine Codes","display_name":"Generalized Hamming Weights for Almost Affine Codes","publication_year":2017,"publication_date":"2017-01-17","ids":{"openalex":"https://openalex.org/W2270827087","doi":"https://doi.org/10.1109/tit.2017.2654456","mag":"2270827087"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2654456","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2654456","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.01504","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Trygve Johnsen","orcid":null},"institutions":[{"id":"https://openalex.org/I78037679","display_name":"UiT The Arctic University of Norway","ror":"https://ror.org/00wge5k78","country_code":"NO","type":"education","lineage":["https://openalex.org/I78037679"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Trygve Johnsen","raw_affiliation_strings":["Department of Mathematics and Statistics, UiT The Arctic University of Norway, Troms\u00f8, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, UiT The Arctic University of Norway, Troms\u00f8, Norway","institution_ids":["https://openalex.org/I78037679"]}]},{"author_position":"last","author":{"id":null,"display_name":"Hugues Verdure","orcid":"https://orcid.org/0000-0002-8422-644X"},"institutions":[{"id":"https://openalex.org/I78037679","display_name":"UiT The Arctic University of Norway","ror":"https://ror.org/00wge5k78","country_code":"NO","type":"education","lineage":["https://openalex.org/I78037679"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Hugues Verdure","raw_affiliation_strings":["Department of Mathematics and Statistics, UiT The Arctic University of Norway, Troms\u00f8, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, UiT The Arctic University of Norway, Troms\u00f8, Norway","institution_ids":["https://openalex.org/I78037679"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78037679"],"apc_list":null,"apc_paid":null,"fwci":2.2849,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.90620618,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"63","issue":"4","first_page":"1941","last_page":"1953"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.867900013923645,"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":0.867900013923645,"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":0.04670000076293945,"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"}},{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.022700000554323196,"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/affine-transformation","display_name":"Affine transformation","score":0.7350000143051147},{"id":"https://openalex.org/keywords/hamming","display_name":"Hamming(7,4)","score":0.6498000025749207},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.6193000078201294},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.6080999970436096},{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.6065999865531921},{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.5794000029563904},{"id":"https://openalex.org/keywords/affine-combination","display_name":"Affine combination","score":0.5695000290870667},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5618000030517578}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7512999773025513},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7350000143051147},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.6498000025749207},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.6193000078201294},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6080999970436096},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.6065999865531921},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.5794000029563904},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.5695000290870667},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5618000030517578},{"id":"https://openalex.org/C112128483","wikidata":"https://www.wikidata.org/wiki/Q382504","display_name":"Affine hull","level":4,"score":0.5367000102996826},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5171999931335449},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4830000102519989},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45339998602867126},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.43459999561309814},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.33869999647140503},{"id":"https://openalex.org/C62623296","wikidata":"https://www.wikidata.org/wiki/Q686291","display_name":"Affine group","level":3,"score":0.3343999981880188},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.287200003862381},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.2727000117301941},{"id":"https://openalex.org/C95565831","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine coordinate system","level":4,"score":0.26579999923706055},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.25360000133514404},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.25}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2017.2654456","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2654456","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:arXiv.org:1601.01504","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.01504","pdf_url":"https://arxiv.org/pdf/1601.01504","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:munin.uit.no:10037/12403","is_oa":true,"landing_page_url":"https://hdl.handle.net/10037/12403","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.01504","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.01504","pdf_url":"https://arxiv.org/pdf/1601.01504","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1520448495","https://openalex.org/W1970845455","https://openalex.org/W1987386982","https://openalex.org/W1991133427","https://openalex.org/W1991338994","https://openalex.org/W1996584657","https://openalex.org/W2003753892","https://openalex.org/W2031058522","https://openalex.org/W2031906711","https://openalex.org/W2083394863","https://openalex.org/W2097117337","https://openalex.org/W2127558904","https://openalex.org/W2144263303","https://openalex.org/W4241576711"],"related_works":[],"abstract_inverted_index":{"We":[0,9],"define":[1],"generalized":[2,25],"Hamming":[3,26],"weights":[4,27],"for":[5,28],"almost":[6,32,42],"affine":[7,33,43],"codes.":[8,34,52],"show":[10],"that":[11],"this":[12],"definition":[13],"is":[14],"natural,":[15],"since":[16],"we":[17,37],"can":[18],"extend":[19],"some":[20],"well-known":[21],"properties":[22],"of":[23,41,46,50],"the":[24,39,47],"linear":[29],"codes,":[30,44],"to":[31],"In":[35],"addition,":[36],"discuss":[38],"duality":[40],"and":[45],"smaller":[48],"class":[49],"multilinear":[51]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2016-06-24T00:00:00"}