{"id":"https://openalex.org/W3007379934","doi":"https://doi.org/10.1109/redundancy48165.2019.9003348","title":"New bounds for linear codes of covering radius 3 and 2-saturating sets in projective spaces","display_name":"New bounds for linear codes of covering radius 3 and 2-saturating sets in projective spaces","publication_year":2019,"publication_date":"2019-10-01","ids":{"openalex":"https://openalex.org/W3007379934","doi":"https://doi.org/10.1109/redundancy48165.2019.9003348","mag":"3007379934"},"language":"en","primary_location":{"id":"doi:10.1109/redundancy48165.2019.9003348","is_oa":false,"landing_page_url":"https://doi.org/10.1109/redundancy48165.2019.9003348","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 XVI International Symposium \"Problems of Redundancy in Information and Control Systems\" (REDUNDANCY)","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/A5018158772","display_name":"Alexander A. Davydov","orcid":"https://orcid.org/0000-0002-5827-4560"},"institutions":[{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Alexander A. Davydov","raw_affiliation_strings":["Institute for Information Transmission Problems (Kharkevich institute), Russian Academy of Sciences, Moscow, Russian Federation"],"affiliations":[{"raw_affiliation_string":"Institute for Information Transmission Problems (Kharkevich institute), Russian Academy of Sciences, Moscow, Russian Federation","institution_ids":["https://openalex.org/I4210107660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028598034","display_name":"Stefano Marcugini","orcid":"https://orcid.org/0000-0002-7961-0260"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Marcugini","raw_affiliation_strings":["Department of Mathematics and Computer Science, Perugia University, Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Perugia University, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010058458","display_name":"Fernanda Pambianco","orcid":"https://orcid.org/0000-0001-5476-5365"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fernanda Pambianco","raw_affiliation_strings":["Department of Mathematics and Computer Science, Perugia University, Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Perugia University, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018158772"],"corresponding_institution_ids":["https://openalex.org/I4210107660"],"apc_list":null,"apc_paid":null,"fwci":0.5601,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76350162,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9993000030517578,"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":0.9993000030517578,"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":0.996999979019165,"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/T10849","display_name":"Finite Group Theory Research","score":0.9815000295639038,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4659598469734192},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37297481298446655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3076222538948059}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4659598469734192},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37297481298446655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3076222538948059}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/redundancy48165.2019.9003348","is_oa":false,"landing_page_url":"https://doi.org/10.1109/redundancy48165.2019.9003348","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 XVI International Symposium \"Problems of Redundancy in Information and Control Systems\" (REDUNDANCY)","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":12,"referenced_works":["https://openalex.org/W59572088","https://openalex.org/W2014025706","https://openalex.org/W2073553414","https://openalex.org/W2093969646","https://openalex.org/W2119257394","https://openalex.org/W2124113125","https://openalex.org/W2210977112","https://openalex.org/W2340949728","https://openalex.org/W2779697196","https://openalex.org/W2903421962","https://openalex.org/W4300972025","https://openalex.org/W6747151314"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"The":[0],"length":[1,12],"function":[2],"l":[3,35,96,104,118,152,243],"<sub":[4,36,65,97,105,119,153,244],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,37,66,98,106,120,127,135,154,161,169,245,252,260],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[6,38,67,99,107,121,155,246],"(r,":[7,39,122,156,247],"R)":[8],"is":[9,225],"the":[10,59,77,84,207,216,230],"smallest":[11],"of":[13,18,86,195,215,218,235],"a":[14],"q-ary":[15],"linear":[16],"code":[17],"covering":[19],"radius":[20],"R":[21,68],"and":[22,70,198],"codimension":[23],"(redundancy)":[24],"r.":[25],"In":[26,112],"this":[27,228],"paper,":[28],"we":[29,57,90,114,189],"obtained":[30],"new":[31,92,219],"upper":[32,93],"bounds":[33,94,232],"on":[34,95,206,212],"3),":[40,103],"r":[41,53,138,172,263],"=":[42,46,54,139,173,264],"3t+1":[43],"\u2265":[44,48,51,143,146,149,177,180,268,271],"4,andr":[45],"3t+2":[47],"5,":[49,178],"t":[50,145,179,270],"1.For":[52],"4,":[55,144,269],"5":[56],"use":[58],"one-to-one":[60],"correspondence":[61],"between":[62],"[n,":[63],"n-r]":[64],"codes":[69],"(R-1)-saturating":[71],"sets":[72],"(e.g.":[73],"complete":[74,196],"arcs)":[75],"in":[76,186,222],"projective":[78],"space":[79],"PG(r-1,":[80],"q).":[81],"Then,":[82],"with":[83],"help":[85],"lift-constructions":[87],"increasing":[88],"r,":[89],"obtain":[91],"(3t":[100,108],"+":[101,109,141,175,266],"1,":[102,147,181],"2,":[110],"3).":[111],"particular,":[113],"show":[115],"that":[116,200],"p":[117,151],"3)":[123,157,248],"<;":[124,158,249],"2.7":[125],"<sup":[126,134,160,168,251,259],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sup>":[128,162,253],"\u221a":[129,163,254],"ln":[130,164,255],"q":[131,133,148,165,167,182,256,258],"\u00b7":[132,166,257],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(r-3)/3</sup>":[136,170,261],",":[137,171,262],"3t":[140,174,265],"1":[142,267],"6553;":[150],"2.9":[159],"2":[176],"\u2264":[183],"839.":[184],"Also,":[185],"PG(3,":[187],"q)":[188],"consider":[190],"an":[191,213],"iterative":[192],"step-by-step":[193],"construction":[194],"arcs":[197],"prove":[199],"uncovered":[201],"points":[202,221],"are":[203,241],"evenly":[204],"placed":[205],"space.":[208],"A":[209],"natural":[210],"conjecture":[211],"estimate":[214],"number":[217],"covered":[220],"every":[223],"step":[224],"done.":[226],"Under":[227],"conjecture,":[229],"following":[231],"for":[233],"values":[234],"q,":[236],"not":[237],"limited":[238],"from":[239],"above,":[240],"proposed:":[242],"3":[250],"1.":[272]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
