{"id":"https://openalex.org/W2903702749","doi":"https://doi.org/10.1016/j.endm.2018.11.004","title":"On the Rank of Z8-linear Hadamard Codes","display_name":"On the Rank of Z8-linear Hadamard Codes","publication_year":2018,"publication_date":"2018-12-01","ids":{"openalex":"https://openalex.org/W2903702749","doi":"https://doi.org/10.1016/j.endm.2018.11.004","mag":"2903702749"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.endm.2018.11.004","pdf_url":null,"source":{"id":"https://openalex.org/S902237881","display_name":"Electronic Notes in Discrete Mathematics","issn_l":"1571-0653","issn":["1571-0653"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5065292754","display_name":"Cristina Fern\u00e1ndez-C\u00f3rdoba","orcid":"https://orcid.org/0000-0001-5880-144X"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Cristina Fern\u00e1ndez-C\u00f3rdoba","raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain"]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055663506","display_name":"Carlos Vela","orcid":"https://orcid.org/0000-0003-3362-8817"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Carlos Vela","raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain"]},{"author_position":"last","author":{"id":"https://openalex.org/A5080668151","display_name":"Merc\u00e8 Villanueva","orcid":"https://orcid.org/0000-0001-6179-0833"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Merc\u00e8 Villanueva","raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain"]}],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065292754","https://openalex.org/A5055663506","https://openalex.org/A5080668151"],"corresponding_institution_ids":["https://openalex.org/I123044942","https://openalex.org/I123044942","https://openalex.org/I123044942"],"apc_list":null,"apc_paid":null,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":1,"cited_by_percentile_year":{"min":68,"max":75},"biblio":{"volume":"70","issue":null,"first_page":"25","last_page":"30"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Cryptography and Error-Correcting Codes","score":0.9999,"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":"Cryptography and Error-Correcting Codes","score":0.9999,"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":"Optical Code Division Multiple Access","score":0.9993,"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/T10849","display_name":"Study of Finite Groups and Graphs","score":0.9887,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"keyword":"rank","score":0.3973},{"keyword":"codes","score":0.3926}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7519573},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5650721},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.53302693},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.51113325},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42662087},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.42318216},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39408392},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07645118}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.endm.2018.11.004","pdf_url":null,"source":{"id":"https://openalex.org/S902237881","display_name":"Electronic Notes in Discrete Mathematics","issn_l":"1571-0653","issn":["1571-0653"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad","award_id":"TIN2016-77918-P"},{"funder":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad","award_id":"MTM2015-69138-REDT"}],"referenced_works_count":7,"referenced_works":["https://openalex.org/W1987121126","https://openalex.org/W2038681062","https://openalex.org/W2064737342","https://openalex.org/W2081939650","https://openalex.org/W2109887866","https://openalex.org/W2395800580","https://openalex.org/W2892003982"],"related_works":["https://openalex.org/W2015540166","https://openalex.org/W1666143004","https://openalex.org/W4297787022","https://openalex.org/W78494858","https://openalex.org/W2949126640","https://openalex.org/W2071370397","https://openalex.org/W4321242394","https://openalex.org/W2086435982","https://openalex.org/W1982241170","https://openalex.org/W2386549147"],"ngrams_url":"https://api.openalex.org/works/W2903702749/ngrams","abstract_inverted_index":{"The":[0],"Z2s-additive":[1,38],"codes":[2,16,77,100,135],"are":[3],"subgroups":[4],"of":[5,14,36,50,71,74,78,89,98,116,132],"Z2sn,":[6],"and":[7,19,91],"can":[8,53],"be":[9,54],"seen":[10],"as":[11],"a":[12,26,37,58,83,120],"generalization":[13],"linear":[15],"over":[17],"Z2":[18],"Z4.":[20],"A":[21],"Z2s-linear":[22,75],"Hadamard":[23,28,64,76],"code":[24,29],"is":[25,31,41,101,107,125,136],"binary":[27],"which":[30],"the":[32,45,48,51,62,69,72,96,114,117,130],"Gray":[33],"map":[34],"image":[35],"code.":[39],"It":[40],"known":[42],"that":[43,109],"either":[44],"rank":[46,97],"or":[47],"dimension":[49,70,115],"kernel":[52,73],"used":[55],"to":[56],"give":[57],"complete":[59,84,121],"classification":[60,85],"for":[61,86,103],"Z4-linear":[63],"codes.":[65],"However,":[66],"when":[67],"s>2,":[68],"length":[79],"2t":[80],"only":[81],"provides":[82,119],"some":[87],"values":[88],"t":[90],"s.":[92],"In":[93,127],"this":[94,110,128],"paper,":[95],"these":[99],"given":[102],"s=3.":[104],"Moreover,":[105],"it":[106],"shown":[108],"invariant,":[111],"along":[112],"with":[113],"kernel,":[118],"classification,":[122],"once":[123],"t\u22653":[124],"fixed.":[126],"case,":[129],"number":[131],"nonequivalent":[133],"such":[134],"also":[137],"established.":[138]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2903702749","counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2024-02-28T17:47:34.452807","created_date":"2018-12-22"}