{"id":"https://openalex.org/W4226317702","doi":"https://doi.org/10.1109/tit.2022.3167615","title":"Nonlinear Repair of Reed-Solomon Codes","display_name":"Nonlinear Repair of Reed-Solomon Codes","publication_year":2022,"publication_date":"2022-04-14","ids":{"openalex":"https://openalex.org/W4226317702","doi":"https://doi.org/10.1109/tit.2022.3167615"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3167615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3167615","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/A5025677091","display_name":"Roni Con","orcid":"https://orcid.org/0000-0002-0966-3818"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I4210141777","display_name":"Academic College of Tel Aviv-Yafo","ror":"https://ror.org/04cg6c004","country_code":"IL","type":"education","lineage":["https://openalex.org/I4210141777"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Roni Con","raw_affiliation_strings":["Department of Computer Science, Tel Aviv University, Tel Aviv-Yafo, Israel"],"raw_orcid":"https://orcid.org/0000-0002-0966-3818","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Tel Aviv University, Tel Aviv-Yafo, Israel","institution_ids":["https://openalex.org/I4210141777","https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085150941","display_name":"Itzhak Tamo","orcid":"https://orcid.org/0000-0002-8000-0419"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I4210141777","display_name":"Academic College of Tel Aviv-Yafo","ror":"https://ror.org/04cg6c004","country_code":"IL","type":"education","lineage":["https://openalex.org/I4210141777"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Itzhak Tamo","raw_affiliation_strings":["Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv-Yafo, Israel"],"raw_orcid":"https://orcid.org/0000-0002-8000-0419","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv-Yafo, Israel","institution_ids":["https://openalex.org/I4210141777","https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025677091"],"corresponding_institution_ids":["https://openalex.org/I16391192","https://openalex.org/I4210141777"],"apc_list":null,"apc_paid":null,"fwci":1.9974,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.86605144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"68","issue":"8","first_page":"5165","last_page":"5177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":1.0,"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/T11181","display_name":"Advanced Data Storage Technologies","score":1.0,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9958000183105469,"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/T10237","display_name":"Cryptography and Data Security","score":0.9919999837875366,"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/reed\u2013solomon-error-correction","display_name":"Reed\u2013Solomon error correction","score":0.6170302629470825},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5409873127937317},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5339549779891968},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5054051876068115},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4990081787109375},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48750731348991394},{"id":"https://openalex.org/keywords/distributed-data-store","display_name":"Distributed data store","score":0.4663360118865967},{"id":"https://openalex.org/keywords/tornado-code","display_name":"Tornado code","score":0.4648282527923584},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4375165104866028},{"id":"https://openalex.org/keywords/fountain-code","display_name":"Fountain code","score":0.4360288679599762},{"id":"https://openalex.org/keywords/online-codes","display_name":"Online codes","score":0.42868319153785706},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.4199822247028351},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41280269622802734},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4037643074989319},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36365264654159546},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30081456899642944},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.2090958058834076},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.07688474655151367}],"concepts":[{"id":"https://openalex.org/C78065487","wikidata":"https://www.wikidata.org/wiki/Q1061598","display_name":"Reed\u2013Solomon error correction","level":5,"score":0.6170302629470825},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5409873127937317},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5339549779891968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5054051876068115},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4990081787109375},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48750731348991394},{"id":"https://openalex.org/C24885549","wikidata":"https://www.wikidata.org/wiki/Q339678","display_name":"Distributed data store","level":2,"score":0.4663360118865967},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.4648282527923584},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4375165104866028},{"id":"https://openalex.org/C76132124","wikidata":"https://www.wikidata.org/wiki/Q5474786","display_name":"Fountain code","level":5,"score":0.4360288679599762},{"id":"https://openalex.org/C103093684","wikidata":"https://www.wikidata.org/wiki/Q7094069","display_name":"Online codes","level":5,"score":0.42868319153785706},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.4199822247028351},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41280269622802734},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4037643074989319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36365264654159546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30081456899642944},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2090958058834076},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.07688474655151367},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3167615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3167615","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/G2863868470","display_name":null,"funder_award_id":"852953","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G2877989186","display_name":null,"funder_award_id":"1030/15","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"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1496108277","https://openalex.org/W1899006889","https://openalex.org/W1979205928","https://openalex.org/W1990304797","https://openalex.org/W2051793589","https://openalex.org/W2067005190","https://openalex.org/W2069026918","https://openalex.org/W2096296858","https://openalex.org/W2105185344","https://openalex.org/W2105695025","https://openalex.org/W2120770247","https://openalex.org/W2138744797","https://openalex.org/W2141420453","https://openalex.org/W2150620836","https://openalex.org/W2150777202","https://openalex.org/W2154063365","https://openalex.org/W2337134433","https://openalex.org/W2495618919","https://openalex.org/W2580726118","https://openalex.org/W2606114015","https://openalex.org/W2613593521","https://openalex.org/W2898024058","https://openalex.org/W2950353718","https://openalex.org/W2954626013","https://openalex.org/W2962858508","https://openalex.org/W2963582720","https://openalex.org/W2963677325","https://openalex.org/W2963754880","https://openalex.org/W2963781977","https://openalex.org/W3105184929","https://openalex.org/W3106482607","https://openalex.org/W6724150644"],"related_works":["https://openalex.org/W2295671989","https://openalex.org/W2158757493","https://openalex.org/W2976106059","https://openalex.org/W2951717444","https://openalex.org/W2548320471","https://openalex.org/W4297998332","https://openalex.org/W2060232182","https://openalex.org/W3197169861","https://openalex.org/W2124185731","https://openalex.org/W2069554151"],"abstract_inverted_index":{"The":[0],"problem":[1,142],"of":[2,17,53,62,135,143,147,159,177,182],"repairing":[3],"linear":[4,107,114,198],"codes":[5,12,64,161,209],"and,":[6],"in":[7,19,82],"particular,":[8],"Reed":[9],"Solomon":[10],"(RS)":[11],"has":[13],"attracted":[14],"a":[15,34,51,87,124,178,191,218],"lot":[16],"attention":[18],"recent":[20],"years":[21],"due":[22],"to":[23,27,40],"their":[24],"extreme":[25],"importance":[26],"distributed":[28],"storage":[29],"systems.":[30],"In":[31],"this":[32],"problem,":[33],"failed":[35],"code":[36,184],"symbol":[37],"(node)":[38],"needs":[39],"be":[41],"repaired":[42],"by":[43,120,123,127,216],"downloading":[44],"as":[45,48],"little":[46],"information":[47],"possible":[49],"from":[50],"subset":[52],"the":[54,74,110,116,133,141,154,169,174,187,204],"remaining":[55],"nodes.":[56],"By":[57],"now,":[58],"there":[59],"are":[60,105,113,153],"examples":[61],"RS":[63,148,160,208],"that":[65,190,203],"have":[66],"efficient":[67],"repair":[68,98,137,145,157,165,180,193],"schemes,":[69,138],"and":[70,122,129,185],"some":[71],"even":[72],"attain":[73],"cut-set":[75,170,205],"bound.":[76],"However,":[77],"these":[78,121],"schemes":[79,146],"fall":[80],"short":[81],"several":[83],"aspects;":[84],"they":[85,104],"require":[86],"considerable":[88],"field":[89],"extension":[90],"degree.":[91],"They":[92],"do":[93],"not":[94,211],"provide":[95],"any":[96,183],"nontrivial":[97],"scheme":[99,158,181,194],"over":[100,115,213],"prime":[101,214],"fields.":[102],"Lastly,":[103,200],"all":[106,197],"repairs,":[108],"i.e.,":[109],"computed":[111],"functions":[112],"base":[117],"field.":[118],"Motivated":[119],"question":[125],"raised":[126],"Guruswami":[128],"Wootters,":[130],"2017,":[131],"on":[132],"power":[134],"nonlinear":[136,144,156,179,192],"we":[139,201],"study":[140],"codes.":[149],"Our":[150],"main":[151],"results":[152],"first":[155,175,188],"with":[162],"asymptotically":[163],"optimal":[164],"bandwidth":[166],"(asymptotically":[167],"matching":[168],"bound).":[171],"This":[172],"is":[173,210],"example":[176,189],"also":[186],"can":[195],"outperform":[196],"ones.":[199],"show":[202],"bound":[206],"for":[207],"tight":[212],"fields":[215],"proving":[217],"tighter":[219],"bound,":[220],"using":[221],"additive":[222],"combinatorics":[223],"ideas.":[224]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
