{"id":"https://openalex.org/W2123782067","doi":"https://doi.org/10.1109/isit.2009.5205292","title":"Packing and covering properties of subspace codes","display_name":"Packing and covering properties of subspace codes","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2123782067","doi":"https://doi.org/10.1109/isit.2009.5205292","mag":"2123782067"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2009.5205292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","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/A5037486046","display_name":"Maximilien Gadouleau","orcid":"https://orcid.org/0000-0003-4701-738X"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Maximilien Gadouleau","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Lehigh University, PA, USA","Department of Electrical and Computer Engineering, Lehigh University, PA 18015, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Lehigh University, PA, USA","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Lehigh University, PA 18015, USA","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101582861","display_name":"Zhiyuan Yan","orcid":"https://orcid.org/0000-0003-2286-2771"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhiyuan Yan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Lehigh University, PA, USA","Department of Electrical and Computer Engineering, Lehigh University, PA 18015, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Lehigh University, PA, USA","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Lehigh University, PA 18015, USA","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037486046"],"corresponding_institution_ids":["https://openalex.org/I186143895"],"apc_list":null,"apc_paid":null,"fwci":0.6857,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73486372,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":null,"first_page":"2867","last_page":"2871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9434999823570251,"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":0.9294000267982483,"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/subspace-topology","display_name":"Subspace topology","score":0.9117128849029541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6677646636962891},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5868021845817566},{"id":"https://openalex.org/keywords/sphere-packing","display_name":"Sphere packing","score":0.524254560470581},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5093987584114075},{"id":"https://openalex.org/keywords/asymptotically-optimal-algorithm","display_name":"Asymptotically optimal algorithm","score":0.5029858946800232},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4938576817512512},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4566537141799927},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42523738741874695},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36127740144729614},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.12176921963691711},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0752210021018982},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07013219594955444}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.9117128849029541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6677646636962891},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5868021845817566},{"id":"https://openalex.org/C183893376","wikidata":"https://www.wikidata.org/wiki/Q900117","display_name":"Sphere packing","level":2,"score":0.524254560470581},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5093987584114075},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.5029858946800232},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4938576817512512},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4566537141799927},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42523738741874695},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36127740144729614},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.12176921963691711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0752210021018982},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07013219594955444},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2009.5205292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","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":16,"referenced_works":["https://openalex.org/W177399933","https://openalex.org/W1568510176","https://openalex.org/W1993359877","https://openalex.org/W2048235391","https://openalex.org/W2055060019","https://openalex.org/W2095547380","https://openalex.org/W2125306810","https://openalex.org/W2125838758","https://openalex.org/W2128555802","https://openalex.org/W2129429315","https://openalex.org/W2130340248","https://openalex.org/W2135643259","https://openalex.org/W2139416652","https://openalex.org/W2141699149","https://openalex.org/W3101800757","https://openalex.org/W4212896000"],"related_works":["https://openalex.org/W1980381208","https://openalex.org/W2364594919","https://openalex.org/W2219338811","https://openalex.org/W2167092671","https://openalex.org/W1861706286","https://openalex.org/W2149583853","https://openalex.org/W1120847856","https://openalex.org/W4293472652","https://openalex.org/W1799971747","https://openalex.org/W2159466585"],"abstract_inverted_index":{"Codes":[0],"in":[1,15,18,33],"the":[2,19,42,55,59,70,80,90,136],"projective":[3,71],"space":[4],"over":[5],"a":[6],"finite":[7],"field,":[8],"referred":[9,21],"to":[10,22,127],"as":[11,23],"subspace":[12,48,56,86,99,115,132],"codes,":[13,49,87],"and":[14,44,84,88,96],"particular":[16],"codes":[17,25,100,116,133],"Grassmannians,":[20],"constant-dimension":[24],"(CDCs),":[26],"have":[27],"been":[28],"proposed":[29],"for":[30,101,117,135],"error":[31],"control":[32],"random":[34],"network":[35],"coding.":[36],"In":[37],"this":[38],"paper,":[39],"we":[40,76],"study":[41],"packing":[43,83,95,109,114],"covering":[45,85,98,122,131],"properties":[46,68],"of":[47,69,82,93],"which":[50],"can":[51,124],"be":[52,125],"used":[53,126],"with":[54],"metric":[57],"or":[58],"injection":[60,137],"metric.":[61,138],"We":[62,104],"first":[63],"determine":[64,89],"some":[65],"fundamental":[66],"geometric":[67],"space.":[72],"Using":[73],"these":[74],"results,":[75],"derive":[77],"bounds":[78],"on":[79],"cardinalities":[81],"asymptotic":[91],"rate":[92],"optimal":[94,97,108,113,121,130],"both":[102,118],"metrics.":[103,119],"thus":[105],"show":[106],"that":[107],"CDCs":[110,123],"are":[111],"asymptotically":[112,129],"However,":[120],"construct":[128],"only":[134]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}