{"id":"https://openalex.org/W2018009393","doi":"https://doi.org/10.1109/tit.2015.2445758","title":"New Bounds and Constructions for Granular Media Coding","display_name":"New Bounds and Constructions for Granular Media Coding","publication_year":2015,"publication_date":"2015-06-16","ids":{"openalex":"https://openalex.org/W2018009393","doi":"https://doi.org/10.1109/tit.2015.2445758","mag":"2018009393"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2445758","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2445758","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":"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/A5029931391","display_name":"Artyom Sharov","orcid":"https://orcid.org/0000-0001-9120-8314"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Artyom Sharov","raw_affiliation_strings":["Department of Computer Science, Technion\u2013Israel Institute of Technology, Haifa, Israel","[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion\u2013Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074098103","display_name":"Ron M. Roth","orcid":"https://orcid.org/0000-0003-4168-9505"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ron M. Roth","raw_affiliation_strings":["Department of Computer Science, Technion\u2013Israel Institute of Technology, Haifa, Israel","[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion\u2013Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.4016,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.67153069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"61","issue":"8","first_page":"4227","last_page":"4238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11130","display_name":"Coding theory and cryptography","score":0.996999979019165,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7777853012084961},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6191403269767761},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5802152156829834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5108973383903503},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.44492557644844055},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4402584433555603},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.43907737731933594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1902121603488922},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18638789653778076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07732301950454712}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7777853012084961},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6191403269767761},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5802152156829834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5108973383903503},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.44492557644844055},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4402584433555603},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.43907737731933594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1902121603488922},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18638789653778076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07732301950454712},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2015.2445758","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2445758","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2873328723","display_name":null,"funder_award_id":"1092/12","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W137846029","https://openalex.org/W1606480398","https://openalex.org/W1966525046","https://openalex.org/W1970327862","https://openalex.org/W1984313720","https://openalex.org/W2003177806","https://openalex.org/W2005919832","https://openalex.org/W2014543054","https://openalex.org/W2015385212","https://openalex.org/W2015653910","https://openalex.org/W2017358938","https://openalex.org/W2031539615","https://openalex.org/W2034672123","https://openalex.org/W2037860461","https://openalex.org/W2041588219","https://openalex.org/W2049880801","https://openalex.org/W2050453090","https://openalex.org/W2071609006","https://openalex.org/W2072732436","https://openalex.org/W2081130995","https://openalex.org/W2087567316","https://openalex.org/W2098922615","https://openalex.org/W2099111195","https://openalex.org/W2100088314","https://openalex.org/W2100774975","https://openalex.org/W2115348876","https://openalex.org/W2123080044","https://openalex.org/W2126375604","https://openalex.org/W2130594164","https://openalex.org/W2139311046","https://openalex.org/W2141461561","https://openalex.org/W2142034042","https://openalex.org/W2151286572","https://openalex.org/W2151792913","https://openalex.org/W2152042087","https://openalex.org/W2158477630","https://openalex.org/W2160997130","https://openalex.org/W2296034829","https://openalex.org/W2963183421","https://openalex.org/W3101393421","https://openalex.org/W3103229293","https://openalex.org/W3142300713","https://openalex.org/W4231806134","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W1495042958","https://openalex.org/W2494338568","https://openalex.org/W2122678784","https://openalex.org/W2282510344","https://openalex.org/W139987158","https://openalex.org/W2183994405","https://openalex.org/W1875646599","https://openalex.org/W1976807322","https://openalex.org/W2171635774","https://openalex.org/W2129090975"],"abstract_inverted_index":{"Improved":[0],"lower":[1,17,37,89,147],"and":[2,8,29,86,127],"upper":[3,60,67,103],"bounds":[4,38,61,68,104],"on":[5,32,39,49,63,69,79,106,112,134,156],"the":[6,9,33,40,50,56,64,70,80,88,107,113,157],"size":[7,115],"rate":[10,42,72],"of":[11,43,46,55,73,76,91,116,119,125,130,149,160,163],"grain-correcting":[12],"codes":[13,45,75,118,132,162],"are":[14,138],"presented.":[15,167],"The":[16],"bound":[18,90,148],"is":[19,166],"Gilbert-Varshamov-like":[20],"combined":[21],"with":[22],"a":[23,99,135,146],"construction":[24],"by":[25],"Gabrys":[26],"et":[27],"al.,":[28],"it":[30],"improves":[31,62],"previously":[34,108],"best":[35,65,109],"known":[36,66,110],"asymptotic":[41,71],"\u2308\u03c4n\u2309-grain-correcting":[44,74],"length":[47,77,120,164],"n":[48,78,126,155,165],"interval":[51,81],"[0,":[52],"0.0668].":[53],"One":[54],"two":[57],"newly":[58],"presented":[59,139],"\u03c4":[82,94],"\u2208":[83],"(0,":[84],"1/8]":[85],"meets":[87],"1/2":[92,150],"for":[93,122,140],"\u2265":[95],"1/8.":[96],"Moreover,":[97],"in":[98],"nonasymptotic":[100],"regime,":[101],"both":[102],"improve":[105],"results":[111],"largest":[114],"t-grain-correcting":[117],"n,":[121],"certain":[123],"values":[124],"t.":[128],"Constructions":[129],"1-grain-correcting":[131],"based":[133],"partitioning":[136],"technique":[137],"lengths":[141],"up":[142],"to":[143],"18.":[144],"Finally,":[145],"log":[151],"<sub":[152],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[153],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[154],"minimum":[158],"redundancy":[159],"\u221e-grain-detecting":[161]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}