{"id":"https://openalex.org/W3196378311","doi":"https://doi.org/10.1109/isit45174.2021.9517725","title":"On the Linearity and Structure of Z <sub>2</sub> s-Linear Simplex and MacDonald Codes","display_name":"On the Linearity and Structure of Z <sub>2</sub> s-Linear Simplex and MacDonald Codes","publication_year":2021,"publication_date":"2021-07-12","ids":{"openalex":"https://openalex.org/W3196378311","doi":"https://doi.org/10.1109/isit45174.2021.9517725","mag":"3196378311"},"language":"en","primary_location":{"id":"doi:10.1109/isit45174.2021.9517725","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/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"]},{"id":"https://openalex.org/I4210129656","display_name":"Centre for Research on Ecology and Forestry Applications","ror":"https://ror.org/03abrgd14","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210129656","https://openalex.org/I4387153040"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Cristina Fern\u00e1ndez-C\u00f3rdoba","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Cerdanyola del Vall&#x00E8;s,Spain,08193","Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Cerdanyola del Vall&#x00E8;s,Spain,08193","institution_ids":["https://openalex.org/I4210129656"]},{"raw_affiliation_string":"Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"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"]},{"id":"https://openalex.org/I4210129656","display_name":"Centre for Research on Ecology and Forestry Applications","ror":"https://ror.org/03abrgd14","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210129656","https://openalex.org/I4387153040"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Carlos Vela","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Cerdanyola del Vall&#x00E8;s,Spain,08193","Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Cerdanyola del Vall&#x00E8;s,Spain,08193","institution_ids":["https://openalex.org/I4210129656"]},{"raw_affiliation_string":"Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"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"]},{"id":"https://openalex.org/I4210129656","display_name":"Centre for Research on Ecology and Forestry Applications","ror":"https://ror.org/03abrgd14","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210129656","https://openalex.org/I4387153040"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Merc\u00e8 Villanueva","raw_affiliation_strings":["Universitat Aut&#x00F2;noma de Barcelona,Cerdanyola del Vall&#x00E8;s,Spain,08193","Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Aut&#x00F2;noma de Barcelona,Cerdanyola del Vall&#x00E8;s,Spain,08193","institution_ids":["https://openalex.org/I4210129656"]},{"raw_affiliation_string":"Universitat Aut\u00f2noma de Barcelona, Cerdanyola del Vall\u00e8s, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1399,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55883093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"796","last_page":"800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9927999973297119,"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":0.9871000051498413,"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/algorithm","display_name":"Algorithm","score":0.32961633801460266},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31674724817276}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32961633801460266},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31674724817276}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit45174.2021.9517725","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W194960238","https://openalex.org/W1503013413","https://openalex.org/W1516318957","https://openalex.org/W1579261672","https://openalex.org/W1584208130","https://openalex.org/W1606480398","https://openalex.org/W1683886983","https://openalex.org/W1964495070","https://openalex.org/W1976673628","https://openalex.org/W1987121126","https://openalex.org/W2015797376","https://openalex.org/W2038681062","https://openalex.org/W2047094327","https://openalex.org/W2062142782","https://openalex.org/W2064737342","https://openalex.org/W2071383517","https://openalex.org/W2103971511","https://openalex.org/W2109887866","https://openalex.org/W2146744191","https://openalex.org/W2395800580","https://openalex.org/W2889940767","https://openalex.org/W2892003982","https://openalex.org/W2937251225","https://openalex.org/W2962972548","https://openalex.org/W2963946634","https://openalex.org/W2990636281","https://openalex.org/W2991239327","https://openalex.org/W2993272705","https://openalex.org/W3048948753","https://openalex.org/W3099018150","https://openalex.org/W3106364761","https://openalex.org/W4211147273","https://openalex.org/W4285719527","https://openalex.org/W4300529123","https://openalex.org/W6634985997"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Z":[0,12,31,36,42,66,77,115,172],"<inf":[1,16,32,37,43,67,78,98,116,143,173],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,5,14,17,33,38,44,47,68,71,79,96,99,102,117,120,141,144,174,177,186],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>":[3,18,34,45,69,80,100,118,145,175],"<tex":[4,46,70,95,101,119,140,176,185],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$s$</tex>":[6,48,72,103,121,178,187],"-additive":[7,73,122,179],"codes":[8,29,84,110,155,181],"are":[9,91,111,182,193],"subgroups":[10],"of":[11,27,64,85,104,137,153,158,168],"<sup":[13],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[15],"s,":[19],"and":[20,35,88,150,190],"can":[21],"be":[22],"seen":[23],"as":[24,156],"a":[25,52,65,87,92,134,151],"generalization":[26,93],"linear":[28,135],"over":[30,94],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4</inf>":[39],".":[40],"A":[41],"-linear":[49],"code":[50,54],"is":[51,59],"binary":[53,106],"(not":[55],"necessarily":[56],"linear)":[57],"which":[58,90],"the":[60,105,114,138,166],"Gray":[61],"map":[62],"image":[63],"code.":[74],"We":[75],"consider":[76],"s-":[81],"additive":[82],"simplex":[83,107],"type":[86],"\u03b2,":[89],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$Z$</tex>":[97,142],"codes.":[108,124,170],"These":[109],"related":[112],"to":[113,132],"Hadamard":[123],"In":[125,161],"this":[126,130,159,163],"paper,":[127],"we":[128],"use":[129],"relationship":[131],"find":[133],"subcode":[136],"corresponding":[139],"s-linear":[146],"codes,":[147],"called":[148],"kernel,":[149],"representation":[152],"these":[154,169],"cosets":[157],"kernel.":[160],"particular,":[162],"also":[164],"gives":[165],"linearity":[167],"Similarly,":[171],"MacDonald":[180],"defined":[183],"for":[184],">":[188],"2,":[189],"equivalent":[191],"results":[192],"obtained.":[194]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
