{"id":"https://openalex.org/W2171704677","doi":"https://doi.org/10.1109/netcod.2009.5191396","title":"On error control codes for random network coding","display_name":"On error control codes for random network coding","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2171704677","doi":"https://doi.org/10.1109/netcod.2009.5191396","mag":"2171704677"},"language":"en","primary_location":{"id":"doi:10.1109/netcod.2009.5191396","doi":"https://doi.org/10.1109/netcod.2009.5191396","is_oa":false,"landing_page_url":"https://doi.org/10.1109/netcod.2009.5191396","pdf_url":null,"source":{"id":"https://openalex.org/S7407086623","display_name":"International Symposium on Network Coding (NetCod)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 Workshop on Network Coding, Theory, and Applications","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","is_traditional":true,"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/A5038318637","display_name":"Rudolf Ahlswede","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"R. Ahlswede","raw_affiliation_strings":["Department of Mathematics, University of Bielefeld, Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bielefeld, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110058646","display_name":"H. Aydinian","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"H. Aydinian","raw_affiliation_strings":["Department of Mathematics, University of Bielefeld, Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bielefeld, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20121455"],"apc_list":null,"apc_paid":null,"fwci":5.5474,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.96818182,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"68","last_page":"73"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9042999744415283,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9042999744415283,"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"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.06830000132322311,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.006300000008195639,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/random-linear-network-coding","display_name":"random linear network coding","score":0.9440000057220459},{"id":"https://openalex.org/keywords/error-correcting-codes","display_name":"error-correcting codes","score":0.7409999966621399},{"id":"https://openalex.org/keywords/subspace-codes","display_name":"subspace codes","score":0.8349999785423279},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"dimensionality reduction","score":0.9959999918937683},{"id":"https://openalex.org/keywords/subspace-distance","display_name":"subspace distance","score":0.6230000257492065},{"id":"https://openalex.org/keywords/packet-error","display_name":"packet error","score":0.6539999842643738},{"id":"https://openalex.org/keywords/erasure","display_name":"erasure","score":0.859000027179718},{"id":"https://openalex.org/keywords/adversarial-attacks","display_name":"adversarial attacks","score":0.7720000147819519}],"concepts":[{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.7649682760238647},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6491873264312744},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5825139880180359},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5082880854606628},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.464459627866745},{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.4547525942325592},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4520518481731415},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4329165816307068},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43016698956489563},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.4283030033111572},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4274674355983734},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.4210554361343384},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4202326536178589},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.28294849395751953},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24850744009017944},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.16512715816497803},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08624416589736938},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/netcod.2009.5191396","doi":"https://doi.org/10.1109/netcod.2009.5191396","is_oa":false,"landing_page_url":"https://doi.org/10.1109/netcod.2009.5191396","pdf_url":null,"source":{"id":"https://openalex.org/S7407086623","display_name":"International Symposium on Network Coding (NetCod)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 Workshop on Network Coding, Theory, and Applications","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.321.7127","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.321.7127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-bielefeld.de/ahlswede/homepage/public/231.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W646142101","https://openalex.org/W1568510176","https://openalex.org/W1584248758","https://openalex.org/W1606480398","https://openalex.org/W1996897280","https://openalex.org/W2014554046","https://openalex.org/W2016312880","https://openalex.org/W2048235391","https://openalex.org/W2055060019","https://openalex.org/W2083270107","https://openalex.org/W2088742261","https://openalex.org/W2098313715","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2107712595","https://openalex.org/W2109831419","https://openalex.org/W2125306810","https://openalex.org/W2130350209","https://openalex.org/W2138033161","https://openalex.org/W2139416652","https://openalex.org/W2224932111","https://openalex.org/W2320835389","https://openalex.org/W4298236575"],"related_works":["https://openalex.org/W2189488824","https://openalex.org/W7098413108","https://openalex.org/W1161617264","https://openalex.org/W86443792","https://openalex.org/W7098240887","https://openalex.org/W1502102369","https://openalex.org/W7098121516","https://openalex.org/W2309103680","https://openalex.org/W7099318173","https://openalex.org/W2114622095"],"abstract_inverted_index":{"The":[0],"random":[1,53,97],"network":[2,11,54,98],"coding":[3,108],"approach":[4],"is":[5,15,46],"an":[6],"effective":[7],"technique":[8],"for":[9,60,109,127],"linear":[10],"coding,":[12],"however":[13],"it":[14],"highly":[16],"susceptible":[17],"to":[18,78],"errors":[19,89],"and":[20,25,34,120,125],"adversarial":[21],"attacks.":[22],"Recently":[23],"Kotter":[24],"Kschischang":[26],"introduced":[27],"the":[28,32,79,105],"operator":[29,110],"channel,":[30],"where":[31],"inputs":[33],"outputs":[35],"are":[36,130],"subspaces":[37],"of":[38,81,84,88,107],"a":[39,47],"given":[40],"vector":[41],"space,":[42],"showing":[43],"that":[44],"this":[45,101],"natural":[48],"transmission":[49],"model":[50],"in":[51,95],"noncoherent":[52,96],"coding.":[55,99],"A":[56],"suitable":[57],"metric,":[58],"defined":[59],"subspaces:":[61],"dS(U,":[62],"V":[63,70],")":[64],"=":[65],"dim":[66,69],"U":[67],"+":[68],"-":[71],"2":[72],"dim(U":[73],"cap":[74],"V),":[75],"gives":[76],"rise":[77],"notion":[80],"codes":[82,115,129],"capable":[83],"correcting":[85,116],"different":[86],"kinds":[87],"(like":[90],"packet":[91],"errors,":[92],"erasures":[93],"etc.)":[94],"In":[100],"paper":[102],"we":[103],"continue":[104],"study":[106],"channels":[111],"started.":[112],"We":[113],"consider":[114],"insertions/deletions":[117],"(dimension":[118],"enlargement":[119],"dimension":[121],"reduction":[122],"respectively).":[123],"Bounds":[124],"constructions":[126],"those":[128],"presented.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2016-06-24T00:00:00"}
