{"id":"https://openalex.org/W2087538788","doi":"https://doi.org/10.1109/tit.2014.2359198","title":"Equivalence for Rank-Metric and Matrix Codes and Automorphism Groups of Gabidulin Codes","display_name":"Equivalence for Rank-Metric and Matrix Codes and Automorphism Groups of Gabidulin Codes","publication_year":2014,"publication_date":"2014-09-19","ids":{"openalex":"https://openalex.org/W2087538788","doi":"https://doi.org/10.1109/tit.2014.2359198","mag":"2087538788"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2359198","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2359198","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1304.0501","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073186807","display_name":"Katherine Morrison","orcid":"https://orcid.org/0000-0002-8402-3212"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]},{"id":"https://openalex.org/I71966907","display_name":"University of Northern Colorado","ror":"https://ror.org/016bysn57","country_code":"US","type":"education","lineage":["https://openalex.org/I71966907"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Katherine Morrison","raw_affiliation_strings":["Department of Mathematics, University of Nebraska, Lincoln, NE, USA","School of Mathematical Sciences, University of Northern Colorado, Greeley, CO, USA","Department of Mathematics, University of Nebraska, Lincoln, NE, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska, Lincoln, NE, USA","institution_ids":["https://openalex.org/I114395901"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Northern Colorado, Greeley, CO, USA","institution_ids":["https://openalex.org/I71966907"]},{"raw_affiliation_string":"Department of Mathematics, University of Nebraska, Lincoln, NE, USA#TAB#","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073186807"],"corresponding_institution_ids":["https://openalex.org/I114395901","https://openalex.org/I71966907"],"apc_list":null,"apc_paid":null,"fwci":2.1583,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89246481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"60","issue":"11","first_page":"7035","last_page":"7046"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.996399998664856,"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/T11130","display_name":"Coding theory and cryptography","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7334612011909485},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5513399839401245},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5392739772796631},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.5018022060394287},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.48970654606819153},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4833078384399414},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.4686509966850281},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4638087749481201},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4496135115623474},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.43628358840942383},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.4330879747867584},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40060144662857056},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21660274267196655},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1738884150981903},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.08914387226104736}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7334612011909485},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5513399839401245},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5392739772796631},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.5018022060394287},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.48970654606819153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4833078384399414},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.4686509966850281},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4638087749481201},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4496135115623474},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.43628358840942383},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.4330879747867584},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40060144662857056},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21660274267196655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1738884150981903},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.08914387226104736},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2014.2359198","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2359198","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:1304.0501","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.0501","pdf_url":"https://arxiv.org/pdf/1304.0501","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":"mag:2087538788","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1304.0501","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":"doi:10.48550/arxiv.1304.0501","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1304.0501","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":"pmh:oai:arXiv.org:1304.0501","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.0501","pdf_url":"https://arxiv.org/pdf/1304.0501","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":[{"id":"https://openalex.org/G4546417886","display_name":null,"funder_award_id":"DMS-0838463","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5440069865","display_name":null,"funder_award_id":"DMS-0903517","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6347451225","display_name":null,"funder_award_id":"P200A090002","funder_id":"https://openalex.org/F4320306106","funder_display_name":"U.S. Department of Education"},{"id":"https://openalex.org/G6734009398","display_name":null,"funder_award_id":"DMS-0735099","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306106","display_name":"U.S. Department of Education","ror":"https://ror.org/021adze67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2087538788.pdf","grobid_xml":"https://content.openalex.org/works/W2087538788.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W192485025","https://openalex.org/W1617868970","https://openalex.org/W2011881257","https://openalex.org/W2017022788","https://openalex.org/W2031230255","https://openalex.org/W2048235391","https://openalex.org/W2055060019","https://openalex.org/W2094420277","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2138928022","https://openalex.org/W2139416652","https://openalex.org/W2140204181","https://openalex.org/W2329504308","https://openalex.org/W6607824917","https://openalex.org/W6633675419","https://openalex.org/W6636427457"],"related_works":["https://openalex.org/W2964100779","https://openalex.org/W801938020","https://openalex.org/W2962726324","https://openalex.org/W2762207129","https://openalex.org/W2964936392","https://openalex.org/W2305450768","https://openalex.org/W3099292029","https://openalex.org/W2964235003","https://openalex.org/W2951134075","https://openalex.org/W2765437810","https://openalex.org/W2963415717","https://openalex.org/W3176678390","https://openalex.org/W2957844565","https://openalex.org/W2604987684","https://openalex.org/W2288356016","https://openalex.org/W2937133663","https://openalex.org/W3048630649","https://openalex.org/W3006944685","https://openalex.org/W3197814966","https://openalex.org/W1783130693"],"abstract_inverted_index":{"For":[0],"a":[1,19,58,89,101,107,138,210,227],"growing":[2],"number":[3],"of":[4,16,32,53,67,79,91,140,151,154,165,172,191,199,213,218,230,234],"applications,":[5],"such":[6,88,158],"as":[7,203],"cellular,":[8],"peer-to-peer,":[9],"and":[10,27,64,76,95,112,119,145,174,225],"sensor":[11],"networks,":[12],"efficient":[13],"error-free":[14],"transmission":[15],"data":[17],"through":[18,106],"network":[20,41],"is":[21,50,84,179],"essential.":[22],"Toward":[23],"this":[24,104,124],"end,":[25],"K\u00f6tter":[26],"Kschischang":[28],"propose":[29],"the":[30,40,51,62,68,74,92,148,152,163,189,196,214,231,235],"use":[31],"subspace":[33,48,81],"codes":[34,49,114,135,173,201,238],"to":[35,72,86,136],"provide":[36],"error":[37],"correction":[38],"in":[39],"coding":[42],"context.":[43],"The":[44],"primary":[45],"construction":[46],"for":[47,103,109,133,142,167],"lifting":[52],"rank-metric":[54,94,111,134,184,200,215],"or":[55],"matrix":[56,96,113,143,177,237],"codes,":[57,82,144,220],"process":[59],"that":[60,156,176,194,239],"preserves":[61],"structural":[63],"distance":[65,120],"properties":[66],"underlying":[69,93],"code.":[70],"Thus,":[71],"characterize":[73,147,188],"structure":[75,118,150],"error-correcting":[77],"capability":[78],"these":[80,168],"it":[83],"valuable":[85],"perform":[87],"characterization":[90,212,229],"codes.":[97,205,243],"This":[98],"paper":[99],"lays":[100],"foundation":[102],"analysis":[105],"framework":[108],"classifying":[110],"based":[115],"on":[116,131],"their":[117],"properties.":[121],"To":[122],"enable":[123],"classification,":[125],"we":[126,146,187,208],"extend":[127],"work":[128,222],"by":[129,223],"Berger":[130],"equivalence":[132,141,166,178,192],"define":[137],"notion":[139],"group":[149,217,233],"collection":[153],"maps":[155,193],"preserve":[157],"equivalence.":[159,185],"We":[160],"then":[161],"compare":[162],"notions":[164],"two":[169],"related":[170],"types":[171],"show":[175],"strictly":[180],"more":[181],"general":[182],"than":[183],"Finally,":[186],"set":[190],"fix":[195],"prominent":[197],"class":[198],"known":[202],"Gabidulin":[204,219,242],"In":[206],"particular,":[207],"give":[209,226],"complete":[211],"automorphism":[216],"correcting":[221],"Berger,":[224],"partial":[228],"matrix-automorphism":[232],"expanded":[236],"arise":[240],"from":[241]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
