{"id":"https://openalex.org/W1942351734","doi":"https://doi.org/10.37236/1047","title":"Covering Codes for Hats-on-a-line","display_name":"Covering Codes for Hats-on-a-line","publication_year":2006,"publication_date":"2006-03-07","ids":{"openalex":"https://openalex.org/W1942351734","doi":"https://doi.org/10.37236/1047","mag":"1942351734"},"language":"en","primary_location":{"id":"doi:10.37236/1047","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1047","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r21/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r21/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071818365","display_name":"Sarang Aravamuthan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114539","display_name":"Tata Technologies (India)","ror":"https://ror.org/01x1wr265","country_code":"IN","type":"company","lineage":["https://openalex.org/I4210086519","https://openalex.org/I4210114539"]},{"id":"https://openalex.org/I55215948","display_name":"Tata Consultancy Services (India)","ror":"https://ror.org/01b9n8m42","country_code":"IN","type":"company","lineage":["https://openalex.org/I4210086519","https://openalex.org/I55215948"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sarang Aravamuthan","raw_affiliation_strings":["Tata Research Development and Design Center, Pune, India","Tata Consultancy Services Limited","Advanced Technology Center, Hyderabad, India"],"affiliations":[{"raw_affiliation_string":"Tata Research Development and Design Center, Pune, India","institution_ids":["https://openalex.org/I4210114539"]},{"raw_affiliation_string":"Tata Consultancy Services Limited","institution_ids":["https://openalex.org/I55215948"]},{"raw_affiliation_string":"Advanced Technology Center, Hyderabad, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024708790","display_name":"Sachin Lodha","orcid":"https://orcid.org/0000-0001-5771-4977"},"institutions":[{"id":"https://openalex.org/I4210114539","display_name":"Tata Technologies (India)","ror":"https://ror.org/01x1wr265","country_code":"IN","type":"company","lineage":["https://openalex.org/I4210086519","https://openalex.org/I4210114539"]},{"id":"https://openalex.org/I55215948","display_name":"Tata Consultancy Services (India)","ror":"https://ror.org/01b9n8m42","country_code":"IN","type":"company","lineage":["https://openalex.org/I4210086519","https://openalex.org/I55215948"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sachin Lodha","raw_affiliation_strings":["Advanced Technology Center, Hyderabad, India","Tata Consultancy Services Limited","Tata Research Development and Design Center, Pune, India"],"affiliations":[{"raw_affiliation_string":"Advanced Technology Center, Hyderabad, India","institution_ids":[]},{"raw_affiliation_string":"Tata Consultancy Services Limited","institution_ids":["https://openalex.org/I55215948"]},{"raw_affiliation_string":"Tata Research Development and Design Center, Pune, India","institution_ids":["https://openalex.org/I4210114539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024708790"],"corresponding_institution_ids":["https://openalex.org/I4210114539","https://openalex.org/I55215948"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.07583776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9983999729156494,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9983999729156494,"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/T11130","display_name":"Coding theory and cryptography","score":0.9958999752998352,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7139517068862915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6289855241775513},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.6205030679702759},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5888769030570984},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4866209924221039},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.397505521774292},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26832520961761475},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.10865098237991333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09313952922821045}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7139517068862915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6289855241775513},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.6205030679702759},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5888769030570984},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4866209924221039},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.397505521774292},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26832520961761475},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.10865098237991333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09313952922821045},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1047","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1047","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r21/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.7444","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.7444","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r21.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1047","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1047","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r21/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1942351734.pdf","grobid_xml":"https://content.openalex.org/works/W1942351734.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W56793145","https://openalex.org/W1564417539","https://openalex.org/W1995875735","https://openalex.org/W2073623937","https://openalex.org/W2139771831","https://openalex.org/W2166578450","https://openalex.org/W2562200845","https://openalex.org/W2993383518","https://openalex.org/W6640147141"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W4288278856","https://openalex.org/W2572370460","https://openalex.org/W1976691234"],"abstract_inverted_index":{"We":[0,144,159],"consider":[1],"a":[2,9,17,26,107,167],"popular":[3],"game":[4,169],"puzzle,":[5],"called":[6,53],"Hats-on-a-line,":[7],"wherein":[8],"warden":[10,172],"has":[11,69],"$n$":[12],"prisoners,":[13,174],"each":[14,29,56,67],"one":[15,198],"wearing":[16],"randomly":[18],"assigned":[19],"black":[20],"or":[21,43],"white":[22],"hat,":[23],"stand":[24],"in":[25,196],"line.":[27,82],"Thus":[28],"prisoner":[30,68],"can":[31,49],"see":[32],"the":[33,51,78,81,92,102,111,123,136,150,154,171,180,229],"colors":[34],"of":[35,44,80,101,113,118,129,182,233,237],"all":[36],"hats":[37],"before":[38],"him,":[39],"but":[40],"not":[41],"his":[42,73],"those":[45],"behind":[46],"him.":[47],"Everyone":[48],"hear":[50],"answer":[52],"out":[54,72],"by":[55],"prisoner.":[57],"Based":[58],"on":[59],"this":[60,119,132,176],"information":[61],"and":[62,140,173,240,243],"without":[63],"any":[64],"further":[65],"communication,":[66],"to":[70,105,179,188,193,200],"call":[71],"hat":[74],"color":[75],"starting":[76],"from":[77,91,166],"back":[79],"If":[83],"he":[84,88,95],"gets":[85],"it":[86],"right,":[87],"is":[89,104,228],"released":[90],"prison,":[93],"otherwise":[94],"remains":[96],"incarcerated":[97],"forever.":[98],"The":[99],"goal":[100],"team":[103],"devise":[106],"strategy":[108,148],"that":[109,164,211],"maximizes":[110],"number":[112,128],"correct":[114],"answers.":[115],"A":[116],"variation":[117],"problem":[120,139,177],"asks":[121],"for":[122,125,161,212],"solution":[124,203],"an":[126,146,201,234],"arbitrary":[127],"colors.":[130],"In":[131],"paper,":[133],"we":[134,209],"study":[135],"standard":[137],"Hats-on-a-line":[138],"its":[141],"natural":[142],"extensions.":[143],"demonstrate":[145],"optimal":[147],"when":[149],"seeing":[151],"radius":[152,156,232],"and/or":[153],"hearing":[155],"are":[157],"limited.":[158],"show":[160,210],"certain":[162],"orderings":[163],"arise":[165],"(simulated)":[168],"between":[170],"how":[175],"relates":[178],"theory":[181],"covering":[183,194,231],"codes.":[184],"Our":[185],"investigations":[186],"lead":[187],"two":[189],"optimization":[190],"problems":[191],"related":[192],"codes":[195],"which":[197],"leads":[199],"exact":[202],"(for":[204],"binary":[205],"codes).":[206],"For":[207],"instance,":[208],"$0":[213],"<":[214,216],"k":[215],"n$,":[217],"$(n-k-d)":[218],"\\le":[219],"\\alpha_m":[220],"n$":[221],"where":[222],"$d":[223],"=":[224,245],"t(n-k,":[225],"m^k,":[226],"m)$":[227],"minimum":[230],"$m$-ary":[235],"code":[236],"length":[238],"($n-k$)":[239],"size":[241],"$m^k$":[242],"$$\\alpha_m":[244],"{\\log":[246],"m\\over":[247],"\\log":[248],"(m^2":[249],"-m":[250],"+1)}.$$":[251]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}