{"id":"https://openalex.org/W279334359","doi":null,"title":"Any Errors in this Dissertation are Probably Fixable: Topics in Probability and Error Correcting Codes.","display_name":"Any Errors in this Dissertation are Probably Fixable: Topics in Probability and Error Correcting Codes.","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W279334359","mag":"279334359"},"language":"en","primary_location":{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/108844","doi":null,"is_oa":false,"landing_page_url":"https://deepblue.lib.umich.edu/bitstreams/80c0b36a-82cf-4f1d-b44f-275c333b3038/download","pdf_url":null,"source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Thesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"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/A5022963784","display_name":"Mary K. Wootters","orcid":"https://orcid.org/0000-0002-2345-2531","observed_orcids":["https://orcid.org/0000-0002-2345-2531"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mary Wootters","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2345-2531","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5022963784"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":0.9678000211715698,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9678000211715698,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.028300000354647636,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0010999999940395355,"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/list-decoding","display_name":"list decoding","score":0.7950000166893005},{"id":"https://openalex.org/keywords/local-decoding","display_name":"local decoding","score":0.9539999961853027},{"id":"https://openalex.org/keywords/error-correcting-codes","display_name":"error-correcting codes","score":0.8320000171661377},{"id":"https://openalex.org/keywords/random-linear-codes","display_name":"random linear codes","score":0.9639999866485596},{"id":"https://openalex.org/keywords/reed-solomon-codes","display_name":"Reed-Solomon codes","score":0.9980000257492065},{"id":"https://openalex.org/keywords/expander-codes","display_name":"expander codes","score":0.8289999961853027},{"id":"https://openalex.org/keywords/high-dimensional-probability","display_name":"high-dimensional probability","score":0.8989999890327454},{"id":"https://openalex.org/keywords/code-ensembles","display_name":"code ensembles","score":0.5849999785423279}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4142056405544281},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3503473699092865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3490634560585022},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3465110659599304}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/108844","doi":null,"is_oa":false,"landing_page_url":"https://deepblue.lib.umich.edu/bitstreams/80c0b36a-82cf-4f1d-b44f-275c333b3038/download","pdf_url":null,"source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Thesis"},{"id":"mag:279334359","doi":null,"is_oa":false,"landing_page_url":"https://deepblue.lib.umich.edu/bitstream/2027.42/108844/1/wootters_1.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":95,"referenced_works":["https://openalex.org/W105861178","https://openalex.org/W143004564","https://openalex.org/W279095530","https://openalex.org/W284999918","https://openalex.org/W286346820","https://openalex.org/W1481582196","https://openalex.org/W1492537195","https://openalex.org/W1496108277","https://openalex.org/W1511939522","https://openalex.org/W1556782625","https://openalex.org/W1559980198","https://openalex.org/W1573296009","https://openalex.org/W1589182929","https://openalex.org/W1593251595","https://openalex.org/W1606480398","https://openalex.org/W1840524043","https://openalex.org/W1901622511","https://openalex.org/W1965633735","https://openalex.org/W1967907222","https://openalex.org/W1970056983","https://openalex.org/W1970912697","https://openalex.org/W1979019025","https://openalex.org/W1980073965","https://openalex.org/W1991736637","https://openalex.org/W1994091697","https://openalex.org/W1995875735","https://openalex.org/W1998698985","https://openalex.org/W1999230097","https://openalex.org/W2000211775","https://openalex.org/W2001903189","https://openalex.org/W2005460996","https://openalex.org/W2014712128","https://openalex.org/W2014860393","https://openalex.org/W2016047221","https://openalex.org/W2018047324","https://openalex.org/W2027528470","https://openalex.org/W2029859729","https://openalex.org/W2030633623","https://openalex.org/W2034970974","https://openalex.org/W2036602082","https://openalex.org/W2036871172","https://openalex.org/W2045503106","https://openalex.org/W2046101558","https://openalex.org/W2048651540","https://openalex.org/W2052755788","https://openalex.org/W2053086236","https://openalex.org/W2054496431","https://openalex.org/W2055064119","https://openalex.org/W2055656009","https://openalex.org/W2061949491","https://openalex.org/W2065151783","https://openalex.org/W2068593329","https://openalex.org/W2089272132","https://openalex.org/W2090418561","https://openalex.org/W2092243741","https://openalex.org/W2094878497","https://openalex.org/W2096915068","https://openalex.org/W2102212547","https://openalex.org/W2106215079","https://openalex.org/W2107764994","https://openalex.org/W2109831361","https://openalex.org/W2116231125","https://openalex.org/W2121417875","https://openalex.org/W2121825730","https://openalex.org/W2128765501","https://openalex.org/W2130217481","https://openalex.org/W2133068391","https://openalex.org/W2133589924","https://openalex.org/W2135393523","https://openalex.org/W2137806147","https://openalex.org/W2138236884","https://openalex.org/W2139964991","https://openalex.org/W2142293082","https://openalex.org/W2143299189","https://openalex.org/W2145012723","https://openalex.org/W2145273667","https://openalex.org/W2146078064","https://openalex.org/W2146220490","https://openalex.org/W2148575324","https://openalex.org/W2152380194","https://openalex.org/W2154198326","https://openalex.org/W2154522281","https://openalex.org/W2162449851","https://openalex.org/W2162725776","https://openalex.org/W2168219305","https://openalex.org/W2171486154","https://openalex.org/W2174870427","https://openalex.org/W2177108502","https://openalex.org/W2224258886","https://openalex.org/W2242452602","https://openalex.org/W2293231900","https://openalex.org/W2567264041","https://openalex.org/W2950426762","https://openalex.org/W3004537778","https://openalex.org/W3037365189"],"related_works":["https://openalex.org/W1918170838","https://openalex.org/W304297541","https://openalex.org/W2001659896","https://openalex.org/W4414981966","https://openalex.org/W7098256968","https://openalex.org/W2125708265","https://openalex.org/W105861178","https://openalex.org/W2973003915","https://openalex.org/W7214825887","https://openalex.org/W1580365030"],"abstract_inverted_index":{"We":[0,10,70],"study":[1],"two":[2,29],"problems":[3,31],"in":[4,18],"coding":[5],"theory,":[6],"list-decoding":[7],"and":[8,51,110,124],"local-decoding.":[9],"take":[11],"a":[12,77],"probabilistic":[13,123],"approach":[14,66],"to":[15,20,74,76,92,108],"these":[16],"problems,":[17],"contrast":[19],"more":[21],"typical":[22],"algebraic":[23],"approaches.":[24],"In":[25,86],"list-decoding,":[26],"we":[27,42,53,88],"settle":[28],"open":[30],"about":[32],"the":[33,114],"list-decodability":[34],"of":[35,39,80],"some":[36],"well-studied":[37],"ensembles":[38],"codes.":[40],"First,":[41],"show":[43,54],"that":[44,55],"random":[45,84],"linear":[46,95],"codes":[47,59,81,91,96,104],"are":[48,61],"optimally":[49,63],"list-decodable,":[50],"second,":[52],"there":[56],"exist":[57],"Reed-Solomon":[58],"which":[60],"(nearly)":[62],"list-decodable.":[64],"Our":[65],"uses":[67],"high-dimensional":[68],"probability.":[69],"extend":[71],"this":[72,112],"framework":[73],"apply":[75],"large":[78],"family":[79],"obtained":[82],"through":[83],"operations.":[85],"local-decoding,":[87],"use":[89],"expander":[90],"construct":[93],"locally-correctible":[94],"with":[97],"rate":[98],"approaching":[99],"1.":[100],"Until":[101],"recently,":[102],"such":[103],"were":[105],"conjectured":[106],"not":[107],"exist,":[109],"before":[111],"work":[113],"only":[115],"known":[116],"constructions":[117],"relied":[118],"on":[119],"algebraic,":[120],"rather":[121],"than":[122],"combinatorial,":[125],"methods.":[126]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}