{"id":"https://openalex.org/W2253043110","doi":"https://doi.org/10.3934/amc.2017018","title":"Rank equivalent and rank degenerate skew cyclic codes","display_name":"Rank equivalent and rank degenerate skew cyclic codes","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2253043110","doi":"https://doi.org/10.3934/amc.2017018","mag":"2253043110"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2017018","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017018","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2017018","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006688702","display_name":"Umberto Mart\u00ednez-Pe\u00f1as","orcid":"https://orcid.org/0000-0003-2626-8139"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Umberto Mart\u00ednez-Pe\u00f1as","raw_affiliation_strings":["Institut for Matematiske Fag, Det Ingeni\u00f8r- og Naturvidenskabelige Fakultet"],"affiliations":[{"raw_affiliation_string":"Institut for Matematiske Fag, Det Ingeni\u00f8r- og Naturvidenskabelige Fakultet","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006688702"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00244038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"2","first_page":"267","last_page":"282"},"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":0.9883999824523926,"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/skew","display_name":"Skew","score":0.8748050928115845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7419346570968628},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.6849948167800903},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6696792244911194},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5146044492721558},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.473201721906662},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.46988916397094727},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.454046368598938},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.45280906558036804},{"id":"https://openalex.org/keywords/polynomial-code","display_name":"Polynomial code","score":0.41469606757164},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4093584418296814},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2234669327735901},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1965908408164978},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08922946453094482},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.06459841132164001}],"concepts":[{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.8748050928115845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7419346570968628},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.6849948167800903},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6696792244911194},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5146044492721558},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.473201721906662},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.46988916397094727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.454046368598938},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.45280906558036804},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.41469606757164},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4093584418296814},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2234669327735901},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1965908408164978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08922946453094482},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.06459841132164001},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3934/amc.2017018","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017018","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1601.06993","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.06993","pdf_url":"https://arxiv.org/pdf/1601.06993","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":"","raw_type":"text"},{"id":"mag:2253043110","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1601.06993.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pure.atira.dk:publications/c5c6e6dd-35f9-4cb5-836f-eda05cd5712b","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/c5c6e6dd-35f9-4cb5-836f-eda05cd5712b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Martinez Pe\u00f1as , U 2017 , ' Rank equivalent and rank degenerate skew cyclic codes ' , Advances in Mathematics of Communication , vol. 11 , no. 2 , pp. 267-282 . https://doi.org/10.3934/amc.2017018","raw_type":"article"},{"id":"doi:10.48550/arxiv.1601.06993","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1601.06993","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/amc.2017018","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017018","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W941231436","https://openalex.org/W1559343931","https://openalex.org/W1574756032","https://openalex.org/W1785358459","https://openalex.org/W1996310087","https://openalex.org/W2108964585","https://openalex.org/W2115550046","https://openalex.org/W2128555802","https://openalex.org/W2151359594","https://openalex.org/W2165029016","https://openalex.org/W2277316735","https://openalex.org/W2331005958","https://openalex.org/W2949441460","https://openalex.org/W2951186276","https://openalex.org/W3102272702","https://openalex.org/W3121772707","https://openalex.org/W4206775542","https://openalex.org/W4236047074","https://openalex.org/W6651930401","https://openalex.org/W6677151316"],"related_works":["https://openalex.org/W2964184785","https://openalex.org/W3121772707","https://openalex.org/W2950289356","https://openalex.org/W2505046677","https://openalex.org/W2031448371","https://openalex.org/W2108964585","https://openalex.org/W3109056685","https://openalex.org/W1982340557","https://openalex.org/W1991869485","https://openalex.org/W2963945674","https://openalex.org/W2262347634","https://openalex.org/W2950458287","https://openalex.org/W1520389133","https://openalex.org/W2957196640","https://openalex.org/W2076526768","https://openalex.org/W2152261617","https://openalex.org/W2963082190","https://openalex.org/W2120165391","https://openalex.org/W2029905326","https://openalex.org/W2732089117"],"abstract_inverted_index":{"Two":[0],"skew":[1,39,52,75,93,129,150],"cyclic":[2,40,53,76,94,111,130,151,159],"codes":[3,41,95,112],"can":[4,153],"be":[5,154],"equivalent":[6,61,146],"for":[7,30,72,113],"the":[8,15,20,31,47,51,106,136],"Hamming":[9],"metric":[10],"only":[11,19],"if":[12],"they":[13],"have":[14],"same":[16],"length,":[17],"and":[18,80,99,121,126],"zero":[21],"code":[22,54,142,152],"is":[23,27,59,144],"degenerate.":[24],"The":[25],"situation":[26],"completely":[28],"different":[29,43,68,88],"rank":[32,36,60,91,107,145],"metric.":[33],"We":[34,86],"study":[35],"equivalences":[37],"between":[38],"of":[42,49,55,70,90,110,139],"lengths":[44,115,125],"and,":[45],"with":[46],"aim":[48],"finding":[50],"smallest":[56,137],"length":[57,71,138],"that":[58,135,143],"to":[62,123,127,147],"a":[63,73,140,148,157],"given":[64,74,149],"one,":[65],"we":[66,133],"define":[67],"types":[69],"code,":[77],"relate":[78],"them":[79,82],"compute":[81],"in":[83],"most":[84],"cases.":[85],"give":[87],"characterizations":[89],"degenerate":[92],"using":[96],"conventional":[97],"polynomials":[98],"linearized":[100],"polynomials.":[101],"Some":[102],"known":[103],"results":[104],"on":[105],"weight":[108],"hierarchy":[109],"some":[114],"are":[116],"obtained":[117],"as":[118],"particular":[119],"cases":[120],"extended":[122],"all":[124,128],"codes.":[131],"Finally,":[132],"prove":[134],"linear":[141],"attained":[155],"by":[156],"pseudo-skew":[158],"code.":[160]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
