{"id":"https://openalex.org/W4402673736","doi":"https://doi.org/10.1109/tit.2024.3465218","title":"Efficient Algorithms for Constructing Minimum-Weight Codewords in Some Extended Binary BCH Codes","display_name":"Efficient Algorithms for Constructing Minimum-Weight Codewords in Some Extended Binary BCH Codes","publication_year":2024,"publication_date":"2024-09-20","ids":{"openalex":"https://openalex.org/W4402673736","doi":"https://doi.org/10.1109/tit.2024.3465218"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3465218","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tit.2024.3465218","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/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 R&#x0026;D Center, Tel Aviv, Israel","Samsung Semiconductor Israel R&#x0026;D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel"],"raw_orcid":"https://orcid.org/0000-0003-4502-8093","affiliations":[{"raw_affiliation_string":"Samsung Semiconductor Israel R&#x0026;D Center, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]},{"raw_affiliation_string":"Samsung Semiconductor Israel R&#x0026;D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]}]},{"author_position":"middle","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":false,"raw_author_name":"Yaron Shany","raw_affiliation_strings":["Samsung Semiconductor Israel R&#x0026;D Center, Tel Aviv, Israel","Samsung Semiconductor Israel R&#x0026;D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel"],"raw_orcid":"https://orcid.org/0000-0001-6149-9755","affiliations":[{"raw_affiliation_string":"Samsung Semiconductor Israel R&#x0026;D Center, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]},{"raw_affiliation_string":"Samsung Semiconductor Israel R&#x0026;D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]}]},{"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/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":"Itzhak Tamo","raw_affiliation_strings":["Samsung Semiconductor Israel R&#x0026;D Center, Tel Aviv, Israel","Samsung Semiconductor Israel R&#x0026;D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel"],"raw_orcid":"https://orcid.org/0000-0002-8000-0419","affiliations":[{"raw_affiliation_string":"Samsung Semiconductor Israel R&#x0026;D Center, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]},{"raw_affiliation_string":"Samsung Semiconductor Israel R&#x0026;D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210131878"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13108099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"11","first_page":"7673","last_page":"7689"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9068999886512756,"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":0.9068999886512756,"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/bch-code","display_name":"BCH code","score":0.9364254474639893},{"id":"https://openalex.org/keywords/berlekamp\u2013welch-algorithm","display_name":"Berlekamp\u2013Welch algorithm","score":0.6348959803581238},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5097255110740662},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5074207186698914},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.48452991247177124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48187455534935},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.43106791377067566},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4238035976886749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4017730951309204},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.3627588748931885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36270156502723694},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.25004154443740845}],"concepts":[{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.9364254474639893},{"id":"https://openalex.org/C132727834","wikidata":"https://www.wikidata.org/wiki/Q4892328","display_name":"Berlekamp\u2013Welch algorithm","level":5,"score":0.6348959803581238},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5097255110740662},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5074207186698914},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.48452991247177124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48187455534935},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.43106791377067566},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4238035976886749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4017730951309204},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3627588748931885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36270156502723694},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.25004154443740845}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2024.3465218","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tit.2024.3465218","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1588363418","https://openalex.org/W1963935286","https://openalex.org/W1975576968","https://openalex.org/W2034045662","https://openalex.org/W2060709210","https://openalex.org/W2079638931","https://openalex.org/W2080661877","https://openalex.org/W2082608807","https://openalex.org/W2099250555","https://openalex.org/W2146651570","https://openalex.org/W2159757394","https://openalex.org/W2162442687","https://openalex.org/W2790086472","https://openalex.org/W2895239415","https://openalex.org/W2964110229","https://openalex.org/W4252614677","https://openalex.org/W6746610256"],"related_works":["https://openalex.org/W1992183350","https://openalex.org/W2128628822","https://openalex.org/W2361034356","https://openalex.org/W4244153028","https://openalex.org/W1995527419","https://openalex.org/W3021984762","https://openalex.org/W2915572277","https://openalex.org/W2070284141","https://openalex.org/W3133831695","https://openalex.org/W2118665614"],"abstract_inverted_index":{"We":[0,227],"present":[1],"<inline-formula":[2,23,32,42,68,80,96,103,118,132,140,150,157,174,184,195,202,217,246,253,264,272,298,306,313,324,426],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[3,24,33,43,69,81,97,104,119,133,141,151,158,175,185,196,203,218,247,254,265,273,299,307,314,325,427],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[4,25,34,44,70,82,98,105,120,134,142,152,159,176,186,197,204,219,248,255,266,274,300,308,315,326,428],"<tex-math":[5,26,35,45,71,83,99,106,121,135,143,153,160,177,187,198,205,220,249,256,267,275,301,309,316,327,429],"notation=\"LaTeX\">$O(m^{3})$":[6],"</tex-math></inline-formula>":[7,28,37,73,137,181,223,251,303],"algorithms":[8],"for":[9,38,93,116,138,182,192,216,243,290,410,423,485],"specifying":[10],"the":[11,55,60,238,332,336,382,395,399,444,452,464,468,476],"support":[12,56,239],"of":[13,16,21,41,62,67,78,240,283,295,341,347,352,372,386,401,415,443,463,489],"minimum-weight":[14,241,408,469],"codewords":[15,409,470],"extended":[17,291,411],"binary":[18,292,412],"BCH":[19,293,364,370,413],"codes":[20,294,365,371,414],"length":[22],"notation=\"LaTeX\">$n=2^{m}$":[27],"and":[29,75,125,263,285,323,343,354,403,457,478],"designed":[30,94,148,193,244,296,337,374,416,424,487],"distance":[31,95,149,194,245,297,334,417,425,488],"notation=\"LaTeX\">$d(m,s,i):=2^{m-1-s}-2^{m-1-i-s}$":[36],"some":[39,91,361],"values":[40],"notation=\"LaTeX\">$m,i,s$":[46],"</tex-math></inline-formula>,":[47,85,102,110,124,156,165,201,210,262,312,322,432],"where":[48],"m":[49],"may":[50],"grow":[51],"to":[52,236,366],"infinity.":[53],"Here,":[54],"is":[57,379,459],"specified":[58,86],"as":[59,438],"sum":[61],"two":[63],"sets:":[64],"a":[65,76,88,113,126,168,213,348,355,389,434,460,486],"set":[66],"notation=\"LaTeX\">$2^{2i-1}-2^{i-1}$":[72],"elements,":[74],"subspace":[77],"dimension":[79],"notation=\"LaTeX\">$m-2i-s$":[84],"by":[87,225,388,433,455],"basis.":[89],"In":[90,392,447],"detail,":[92],"notation=\"LaTeX\">$6\\cdot":[100,430],"2^{j}$":[101,155,200,431],"notation=\"LaTeX\">$j\\in":[107,161,206],"\\{0,\\ldots":[108,162,207,258],",m-4\\}$":[109],"we":[111,166,211,439,449,471],"have":[112,167,212],"deterministic":[114,214],"algorithm":[115,128,170,215],"even":[117,183],"notation=\"LaTeX\">$m\\geq":[122,188,221,310],"4$":[123,145],"probabilistic":[127,169],"with":[129,171],"success":[130,172],"probability":[131,173],"notation=\"LaTeX\">$1-O(2^{-m})$":[136],"odd":[139],"notation=\"LaTeX\">$m\\gt":[144],"</tex-math></inline-formula>.":[146,190,277],"For":[147],"notation=\"LaTeX\">$28\\cdot":[154],",":[163,208],"m-6\\}$":[164],"notation=\"LaTeX\">$\\geq":[178],"\\frac":[179],"{1}{3}-O(2^{-m/2})$":[180],"6$":[189],"Finally,":[191],"notation=\"LaTeX\">$120\\cdot":[199],"m-8\\}$":[209],"8$":[222],"divisible":[224],"4.":[226],"also":[228,422],"show":[229],"how":[230],"Gold":[231],"functions":[232],"can":[233],"be":[234],"used":[235],"find":[237],"words":[242,362,368],"notation=\"LaTeX\">$d(m,s,i)$":[250,302],"(for":[252,304],"notation=\"LaTeX\">$i\\in":[257],",\\lfloor":[259],"m/2\\rfloor":[260,320],"\\}$":[261],"notation=\"LaTeX\">$s\\leq":[268],"m-2i$":[269,330],"</tex-math></inline-formula>)":[270],"whenever":[271],"notation=\"LaTeX\">$2i|m$":[276],"Our":[278,376],"construction":[279],"builds":[280],"on":[281],"results":[282,400],"Kasami":[284,342],"Lin,":[286],"who":[287,405],"proved":[288],"that":[289,359,451],"integers":[305],"2$":[311],"notation=\"LaTeX\">$0\\leq":[317,328],"i\\leq":[318],"\\lfloor":[319],"$":[321],"s\\leq":[329],"</tex-math></inline-formula>),":[331],"minimum":[333,445],"equals":[335],"distance.":[338,375,446],"The":[339],"proof":[340],"Lin":[344],"makes":[345],"use":[346],"non-constructive":[349,383],"existence":[350],"result":[351],"Berlekamp,":[353],"constructive":[356],"\u201cdown-conversion":[357],"theorem\u201d":[358],"converts":[360],"in":[363,369,380],"lower-weight":[367],"lower":[373],"main":[377],"contribution":[378],"replacing":[381],"counting":[384],"argument":[385],"Berlekamp":[387],"low-complexity":[390],"algorithm.":[391],"one":[393],"aspect,":[394],"current":[396,465],"paper":[397],"extends":[398],"Grigorescu":[402,456],"Kaufman,":[404],"presented":[406],"explicit":[407],"exactly":[418],"6":[419],"(and":[420],"hence":[421],"well-known":[435],"\u201cup-conversion":[436],"theorem\u201d),":[437],"cover":[440],"more":[441],"cases":[442],"fact,":[448],"prove":[450],"codeword":[453],"constructed":[454],"Kaufman":[458],"special":[461],"case":[462],"construction.":[466],"However,":[467],"construct":[472],"do":[473],"not":[474,480],"generate":[475],"code,":[477],"are":[479],"affine":[481],"generators,":[482],"except,":[483],"possibly,":[484],"6.":[490]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}