{"id":"https://openalex.org/W4205701723","doi":"https://doi.org/10.1109/tit.2022.3140678","title":"A Gr\u00f6bner-Bases Approach to Syndrome-Based Fast Chase Decoding of Reed\u2013Solomon Codes","display_name":"A Gr\u00f6bner-Bases Approach to Syndrome-Based Fast Chase Decoding of Reed\u2013Solomon Codes","publication_year":2022,"publication_date":"2022-01-06","ids":{"openalex":"https://openalex.org/W4205701723","doi":"https://doi.org/10.1109/tit.2022.3140678"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3140678","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3140678","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/A5033784450","display_name":"Yaron Shany","orcid":"https://orcid.org/0000-0001-6149-9755"},"institutions":[{"id":"https://openalex.org/I4210131878","display_name":"Samsung (Israel)","ror":"https://ror.org/03k1ymh78","country_code":"IL","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210131878"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yaron Shany","raw_affiliation_strings":["Samsung Semiconductor Israel Research and Development Center, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Samsung Semiconductor Israel Research and Development Center, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057407168","display_name":"A. L. Berman","orcid":"https://orcid.org/0000-0003-4502-8093"},"institutions":[{"id":"https://openalex.org/I4210131878","display_name":"Samsung (Israel)","ror":"https://ror.org/03k1ymh78","country_code":"IL","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210131878"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Amit Berman","raw_affiliation_strings":["Samsung Semiconductor Israel Research and Development Center, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Samsung Semiconductor Israel Research and Development Center, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033784450"],"corresponding_institution_ids":["https://openalex.org/I4210131878"],"apc_list":null,"apc_paid":null,"fwci":0.8336,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76664036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"68","issue":"4","first_page":"2300","last_page":"2318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9990000128746033,"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":0.9969000220298767,"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/decoding-methods","display_name":"Decoding methods","score":0.7092569470405579},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5559238195419312},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5346094369888306},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5048230290412903},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.47993141412734985},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4655405282974243},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4534896910190582},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44839441776275635},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4445972740650177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4092586040496826},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33531323075294495},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.28060001134872437},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1455869972705841},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.11862745881080627},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.07610753178596497}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7092569470405579},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5559238195419312},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5346094369888306},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5048230290412903},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.47993141412734985},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4655405282974243},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4534896910190582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44839441776275635},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4445972740650177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4092586040496826},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33531323075294495},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.28060001134872437},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1455869972705841},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.11862745881080627},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.07610753178596497},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"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":1,"locations":[{"id":"doi:10.1109/tit.2022.3140678","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3140678","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1483218536","https://openalex.org/W1570162207","https://openalex.org/W1606480398","https://openalex.org/W2016746456","https://openalex.org/W2018818965","https://openalex.org/W2023355697","https://openalex.org/W2032431003","https://openalex.org/W2049707341","https://openalex.org/W2066795426","https://openalex.org/W2082281843","https://openalex.org/W2089272132","https://openalex.org/W2091863344","https://openalex.org/W2095026990","https://openalex.org/W2100852839","https://openalex.org/W2102627024","https://openalex.org/W2103811010","https://openalex.org/W2111530591","https://openalex.org/W2124414306","https://openalex.org/W2134791857","https://openalex.org/W2138779125","https://openalex.org/W2144760922","https://openalex.org/W2145362790","https://openalex.org/W2145738710","https://openalex.org/W2153610161","https://openalex.org/W2155020285","https://openalex.org/W2557819255","https://openalex.org/W2895239415","https://openalex.org/W2954976227","https://openalex.org/W2962943736","https://openalex.org/W2981196649","https://openalex.org/W3045546048","https://openalex.org/W3102517494","https://openalex.org/W6633998477","https://openalex.org/W6730259264"],"related_works":["https://openalex.org/W2369600518","https://openalex.org/W2385322349","https://openalex.org/W2351361564","https://openalex.org/W2357077655","https://openalex.org/W1971355272","https://openalex.org/W2387060917","https://openalex.org/W2782734975","https://openalex.org/W2122281830","https://openalex.org/W2370284973","https://openalex.org/W2060592722"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,36,50,61,94,102,137,150,199,224,236,252,256,279],"simple":[3,139,237,258],"syndrome-based":[4,140],"fast":[5,37,141],"Chase":[6,97,103,142,262],"decoding":[7,98,104,143,263],"algorithm":[8,15,39,74,105,239,259,268,276,293],"for":[9,79,162,192,260,282],"Reed\u2013Solomon":[10],"(RS)":[11],"codes.":[12,146,266],"Such":[13],"an":[14],"was":[16],"initially":[17],"presented":[18],"by":[19],"Wu":[20,34],"(IEEE":[21],"Trans.":[22],"IT,":[23],"Jan.":[24],"2012),":[25],"building":[26],"on":[27],"properties":[28],"of":[29,49,83,132,144,148,159,184,208,249,264,286],"the":[30,42,47,125,133,156,181,283,287,291,295,305],"Berlekamp\u2013Massey":[31],"(BM)":[32],"algorithm.":[33,307],"devised":[35],"polynomial-update":[38,73,238],"to":[40,92,217,231,272,304],"construct":[41],"error-locator":[43],"polynomial":[44],"(ELP)":[45],"as":[46,290],"solution":[48,230,284],"certain":[51],"linear-feedback":[52],"shift":[53],"register":[54],"(LFSR)":[55],"synthesis":[56,211],"problem.":[57],"This":[58],"results":[59],"in":[60,90],"conceptually":[62,138,257],"complicated":[63,86],"algorithm,":[64,99],"divided":[65],"into":[66],"8":[67],"subtly":[68],"different":[69],"cases.":[70],"Moreover,":[71],"Wu\u2019s":[72,209],"is":[75,124,136,180,205,214,235,269,300],"not":[76,301],"immediately":[77],"suitable":[78],"working":[80],"with":[81,247,274],"vectors":[82,248],"evaluations.":[84,250],"Therefore,":[85],"modifications":[87],"were":[88],"required":[89],"order":[91],"achieve":[93],"true":[95],"\u201cone-pass\u201d":[96],"that":[100,206,240,277],"is,":[101],"requiring":[106],"<inline-formula":[107,118,165,173,185,193],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[108,119,166,174,186,194,226],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[109,120,167,175,187,195],"<tex-math":[110,121,168,176,188,196],"notation=\"LaTeX\">$O(n)$":[111],"</tex-math></inline-formula>":[112,123,171,179,190,198],"operations":[113],"per":[114],"modified":[115],"coordinate,":[116],"where":[117],"notation=\"LaTeX\">$n$":[122],"RS":[126,145,265],"code":[127],"length.":[128],"The":[129,202,229],"main":[130],"result":[131],"current":[134],"paper":[135],"Instead":[147],"developing":[149],"theory":[151,158],"from":[152],"scratch,":[153],"we":[154,254],"use":[155],"well-established":[157],"Gr\u00f6bner":[160,280],"bases":[161],"modules":[163],"over":[164,223],"notation=\"LaTeX\">$\\mathbb":[169,177],"{F}_{q}[X]$":[170],"(where":[172],"{F}_{q}$":[178],"finite":[182],"field":[183],"notation=\"LaTeX\">$q$":[189,197],"elements,":[191],"prime":[200],"power).":[201],"basic":[203],"observation":[204],"instead":[207],"LFSR":[210],"problem,":[212],"it":[213,299],"much":[215],"simpler":[216],"consider":[218],"\u201cthe":[219],"right\u201d":[220],"minimization":[221,233],"problem":[222,234],"<italic":[225],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">module</i>":[227],".":[228],"this":[232],"avoids":[241],"syndrome":[242],"updates":[243],"and":[244,298],"works":[245],"seamlessly":[246],"As":[251],"result,":[253],"obtain":[255],"one-pass":[261],"Our":[267],"general":[270],"enough":[271],"work":[273],"any":[275],"finds":[278],"basis":[281],"module":[285],"key":[288],"equation":[289],"initial":[292],"(including":[294],"Euclidean":[296],"algorithm),":[297],"tied":[302],"only":[303],"BM":[306]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}
