{"id":"https://openalex.org/W4401693201","doi":"https://doi.org/10.1109/isit57864.2024.10619274","title":"Points-Polynomials Incidence Theorem with an Application to Reed-Solomon Codes","display_name":"Points-Polynomials Incidence Theorem with an Application to Reed-Solomon Codes","publication_year":2024,"publication_date":"2024-07-07","ids":{"openalex":"https://openalex.org/W4401693201","doi":"https://doi.org/10.1109/isit57864.2024.10619274"},"language":"en","primary_location":{"id":"doi:10.1109/isit57864.2024.10619274","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/isit57864.2024.10619274","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Information Theory (ISIT)","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/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"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Itzhak Tamo","raw_affiliation_strings":["Tel Aviv University,Department of Electrical Engineering-Systems,Tel Aviv,Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University,Department of Electrical Engineering-Systems,Tel Aviv,Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085150941"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.112942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3558","last_page":"3563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.984499990940094,"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/reed\u2013solomon-error-correction","display_name":"Reed\u2013Solomon error correction","score":0.6022151112556458},{"id":"https://openalex.org/keywords/incidence","display_name":"Incidence (geometry)","score":0.561995267868042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.423789381980896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.421487420797348},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39808031916618347},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.347969114780426},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2037813365459442},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18547257781028748},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.1794533133506775},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1404833197593689},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.13666069507598877}],"concepts":[{"id":"https://openalex.org/C78065487","wikidata":"https://www.wikidata.org/wiki/Q1061598","display_name":"Reed\u2013Solomon error correction","level":5,"score":0.6022151112556458},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.561995267868042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.423789381980896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.421487420797348},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39808031916618347},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.347969114780426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2037813365459442},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18547257781028748},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.1794533133506775},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1404833197593689},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.13666069507598877},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit57864.2024.10619274","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/isit57864.2024.10619274","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5306423054","display_name":null,"funder_award_id":"852953","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1990524943","https://openalex.org/W1998400388","https://openalex.org/W2040776056","https://openalex.org/W2042431746","https://openalex.org/W2089272132","https://openalex.org/W2098081605","https://openalex.org/W2106215079","https://openalex.org/W2148575324","https://openalex.org/W2150616341","https://openalex.org/W2162725776","https://openalex.org/W2166961358","https://openalex.org/W2461929904","https://openalex.org/W2543082256","https://openalex.org/W3214532196","https://openalex.org/W4245315238","https://openalex.org/W4390092456"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","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/W2129090975"],"abstract_inverted_index":{"This":[0,82],"paper":[1],"focuses":[2],"on":[3,17,42,121],"incidences":[4,22,46],"over":[5],"finite":[6,35],"fields,":[7],"extending":[8],"to":[9,87,91,160],"higher":[10],"degrees":[11],"a":[12,34,40,61,114,133],"result":[13],"by":[14],"Vinh":[15],"[1]":[16],"the":[18,24,43,66,78,92,122,126,129,151],"number":[19,44],"of":[20,45,51,65,77,94,98,107,139,154],"point-line":[21],"in":[23,54,142],"plane":[25],"<tex":[26,30,55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[27,31,56],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathbb{F}^{2}$</tex>,":[28],"where":[29],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathbb{F}$</tex>":[32],"is":[33,84,119],"field.":[36],"Specifically,":[37],"we":[38],"present":[39],"bound":[41,83],"between":[47,69],"points":[48,70],"and":[49,71,125],"polynomials":[50],"bounded":[52],"degree":[53],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathbb{F}^{2}$</tex>.":[57],"Our":[58],"approach":[59],"employs":[60],"singular":[62],"value":[63],"decomposition":[64],"incidence":[67],"matrix":[68],"polynomials,":[72],"coupled":[73],"with":[74,113],"an":[75],"analysis":[76],"related":[79],"group":[80],"algebras.":[81],"then":[85],"applied":[86],"coding":[88],"theory,":[89],"specifically":[90],"problem":[93],"average-radius":[95,111,155],"list":[96,116,135],"decoding":[97],"Reed-Solomon":[99],"(RS)":[100],"codes.":[101],"We":[102],"demonstrate":[103],"that":[104],"RS":[105,140],"codes":[106,141],"certain":[108],"lengths":[109],"are":[110],"list-decodable":[112],"constant":[115,134],"size,":[117],"which":[118],"dependent":[120],"code":[123],"rate":[124],"distance":[127],"from":[128],"Johnson":[130],"radius.":[131],"While":[132],"size":[136],"for":[137,150],"list-decoding":[138,156],"this":[143],"regime":[144],"was":[145,157],"previously":[146],"established,":[147],"its":[148],"existence":[149],"stronger":[152],"notion":[153],"not":[158],"known":[159],"exist.":[161]},"counts_by_year":[],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}