{"id":"https://openalex.org/W2921780681","doi":"https://doi.org/10.1109/tit.2018.2870891","title":"&lt;inline-formula&gt; &lt;tex-math notation=\"LaTeX\"&gt;${\\mathbb{Z}_{2}\\mathbb{Z}_{4}}$ &lt;/tex-math&gt; &lt;/inline-formula&gt;-Additive Cyclic Codes: Kernel and Rank","display_name":"&lt;inline-formula&gt; &lt;tex-math notation=\"LaTeX\"&gt;${\\mathbb{Z}_{2}\\mathbb{Z}_{4}}$ &lt;/tex-math&gt; &lt;/inline-formula&gt;-Additive Cyclic Codes: Kernel and Rank","publication_year":2018,"publication_date":"2018-09-20","ids":{"openalex":"https://openalex.org/W2921780681","doi":"https://doi.org/10.1109/tit.2018.2870891","mag":"2921780681"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2870891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2870891","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":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/record/306142","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050603630","display_name":"Joaquim Borges","orcid":"https://orcid.org/0000-0002-5774-4874"},"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":"Joaquim Borges","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059969175","display_name":"Steven T. Dougherty","orcid":"https://orcid.org/0000-0003-4877-1923"},"institutions":[{"id":"https://openalex.org/I124113063","display_name":"University of Scranton","ror":"https://ror.org/05xwb6v37","country_code":"US","type":"education","lineage":["https://openalex.org/I124113063"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven T. Dougherty","raw_affiliation_strings":["Department of Mathematics, University of Scranton, Scranton, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Scranton, Scranton, PA, USA","institution_ids":["https://openalex.org/I124113063"]}]},{"author_position":"middle","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":false,"raw_author_name":"Cristina Fernandez-Cordoba","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003597169","display_name":"Roger Ten-Valls","orcid":"https://orcid.org/0000-0001-5193-7491"},"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":false,"raw_author_name":"Roger Ten-Valls","raw_affiliation_strings":["Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5050603630"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":null,"apc_paid":null,"fwci":0.1692,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.63774776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"4","first_page":"2119","last_page":"2127"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9965999722480774,"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/rank","display_name":"Rank (graph theory)","score":0.4171954393386841},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38439682126045227},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3751758337020874},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32030826807022095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31995105743408203}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4171954393386841},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38439682126045227},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3751758337020874},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32030826807022095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31995105743408203}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2018.2870891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2870891","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:ddd.uab.cat:306142","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/306142","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"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":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:306142","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/306142","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"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":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1519204501","https://openalex.org/W1579261672","https://openalex.org/W1606480398","https://openalex.org/W1640881979","https://openalex.org/W1882412879","https://openalex.org/W2010238614","https://openalex.org/W2015797376","https://openalex.org/W2038681062","https://openalex.org/W2044522076","https://openalex.org/W2064737342","https://openalex.org/W2071383517","https://openalex.org/W2081939650","https://openalex.org/W2084383186","https://openalex.org/W2118912475","https://openalex.org/W2143250996","https://openalex.org/W2205473711","https://openalex.org/W2320835389","https://openalex.org/W2521253085","https://openalex.org/W2736076565","https://openalex.org/W3101163237"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"A":[0],"\u2124":[1,5,13,21,45,54,96,100,144,148],"<sub":[2,6,14,22,46,55,97,101,145,149],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[3,7,15,18,23,26,47,56,98,102,146,150],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[4,16,48,99,147],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4</sub>":[8,24,57,103,151],"-additive":[9,104,152],"code":[10,72,106,188],"C":[11],"\u2286":[12],"<sup":[17,25],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b1</sup>":[19],"\u00d7":[20],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b2</sup>":[27],"is":[28,131],"called":[29],"cyclic":[30,62,105,171],"if":[31],"the":[32,42,51,65,71,77,86,89,92,110,113,134,174,183,187],"set":[33,43,52],"of":[34,44,53,64,67,82,91,94,112,143,177,182,186],"coordinates":[35,49,66],"can":[36],"be":[37,76],"partitioned":[38],"into":[39],"two":[40],"subsets,":[41],"and":[50,88,118,124,137,159,167,172],"coordinates,":[58],"such":[59],"that":[60,108,133,154,165],"any":[61],"shift":[63],"both":[68],"subsets":[69],"leaves":[70],"invariant.":[73],"Let":[74],"\u03a6(C)":[75],"binary":[78,114,141],"Gray":[79],"map":[80],"image":[81],"C.":[83,189],"We":[84,121],"study":[85],"rank":[87],"dimension":[90],"kernel":[93],"a":[95],"C,":[107],"is,":[109],"dimensions":[111],"linear":[115],"codes":[116,135,153,179],"(\u03a6(C))":[117,136,139],"ker":[119,138],"(\u03a6(C)).":[120],"give":[122],"upper":[123],"lower":[125],"bounds":[126],"for":[127],"these":[128,178],"parameters.":[129],"It":[130],"known":[132],"are":[140,169],"images":[142],"we":[155,163],"denote":[156],"by":[157],"R(C)":[158,166],"K(C),":[160],"respectively.":[161],"Moreover,":[162],"show":[164],"K(C)":[168],"also":[170],"determine":[173],"generator":[175,184],"polynomials":[176,185],"in":[180],"terms":[181]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-03-22T00:00:00"}
