{"id":"https://openalex.org/W2996203760","doi":"https://doi.org/10.1109/tit.2020.3022683","title":"Majority Logic Decoding With Subspace Designs","display_name":"Majority Logic Decoding With Subspace Designs","publication_year":2020,"publication_date":"2020-09-08","ids":{"openalex":"https://openalex.org/W2996203760","doi":"https://doi.org/10.1109/tit.2020.3022683","mag":"2996203760"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2020.3022683","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.3022683","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":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.03344.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034569880","display_name":"Romar dela Cruz","orcid":"https://orcid.org/0000-0003-3563-2262"},"institutions":[{"id":"https://openalex.org/I103911934","display_name":"University of the Philippines System","ror":"https://ror.org/02hqkr514","country_code":"PH","type":"education","lineage":["https://openalex.org/I103911934"]},{"id":"https://openalex.org/I87074743","display_name":"University of the Philippines Diliman","ror":"https://ror.org/03tbh6y23","country_code":"PH","type":"education","lineage":["https://openalex.org/I103911934","https://openalex.org/I87074743"]}],"countries":["PH"],"is_corresponding":false,"raw_author_name":"Romar dela Cruz","raw_affiliation_strings":["Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines","University of the Philippines ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines","institution_ids":["https://openalex.org/I87074743"]},{"raw_affiliation_string":"University of the Philippines ,","institution_ids":["https://openalex.org/I103911934"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025685163","display_name":"Alfred Wassermann","orcid":"https://orcid.org/0000-0001-5946-668X"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alfred Wassermann","raw_affiliation_strings":["Mathematisches Institut, University of Bayreuth, Bayreuth, Germany","University of Bayreuth"],"raw_orcid":"https://orcid.org/0000-0001-5946-668X","affiliations":[{"raw_affiliation_string":"Mathematisches Institut, University of Bayreuth, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]},{"raw_affiliation_string":"University of Bayreuth","institution_ids":["https://openalex.org/I54009628"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0102174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"1","first_page":"179","last_page":"186"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.7159851789474487},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.6072747707366943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5453587770462036},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.508522629737854},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.5019526481628418},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.47434842586517334},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.4596436023712158},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4543816149234772},{"id":"https://openalex.org/keywords/logic-synthesis","display_name":"Logic synthesis","score":0.41884616017341614},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.3848751187324524},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.376173198223114},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.37380483746528625},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36075666546821594},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3105005919933319},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3056313395500183},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08870068192481995}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7159851789474487},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.6072747707366943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5453587770462036},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.508522629737854},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.5019526481628418},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.47434842586517334},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.4596436023712158},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4543816149234772},{"id":"https://openalex.org/C157922185","wikidata":"https://www.wikidata.org/wiki/Q173198","display_name":"Logic synthesis","level":3,"score":0.41884616017341614},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.3848751187324524},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.376173198223114},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.37380483746528625},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36075666546821594},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3105005919933319},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3056313395500183},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08870068192481995},{"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":3,"locations":[{"id":"doi:10.1109/tit.2020.3022683","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.3022683","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"},{"id":"mag:2996203760","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1907.03344.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:eref.uni-bayreuth.de:62474","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/62474/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":{"id":"mag:2996203760","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1907.03344.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1589905506","https://openalex.org/W1658752505","https://openalex.org/W1876525288","https://openalex.org/W2009506926","https://openalex.org/W2088833805","https://openalex.org/W2097385238","https://openalex.org/W2117391034","https://openalex.org/W2121417875","https://openalex.org/W2122165866","https://openalex.org/W2338565441","https://openalex.org/W2791754941","https://openalex.org/W2793807993","https://openalex.org/W2964223061","https://openalex.org/W3194602862","https://openalex.org/W4211147273"],"related_works":["https://openalex.org/W2119973130","https://openalex.org/W2026371176","https://openalex.org/W2040600531","https://openalex.org/W2472661190","https://openalex.org/W3036797629","https://openalex.org/W348408967","https://openalex.org/W63916649","https://openalex.org/W405299824","https://openalex.org/W3040894587","https://openalex.org/W2034035894","https://openalex.org/W3202334878","https://openalex.org/W3136536233","https://openalex.org/W1829344141","https://openalex.org/W79577063","https://openalex.org/W3038078395","https://openalex.org/W2952761579","https://openalex.org/W2293852858","https://openalex.org/W2963664181","https://openalex.org/W3103990458","https://openalex.org/W1918170838"],"abstract_inverted_index":{"Rudolph":[0],"(1967)":[1],"introduced":[2],"one-step":[3],"majority":[4,49,62,82,94],"logic":[5,50,63,83,95],"decoding":[6,84,96],"for":[7],"linear":[8],"codes":[9,69,78,88],"derived":[10],"from":[11,70,89],"combinatorial":[12],"designs.":[13,72],"The":[14],"decoder":[15,51],"is":[16,98,114],"easily":[17],"realizable":[18],"in":[19],"hardware":[20],"and":[21,40],"requires":[22],"that":[23,76],"the":[24,30,53,68,80,87,110],"dual":[25],"code":[26],"has":[27],"to":[28,46],"contain":[29],"blocks":[31],"of":[32,56,107,112],"so":[33],"called":[34],"geometric":[35,90],"designs":[36,109],"as":[37,58,86],"codewords.":[38],"Peterson":[39],"Weldon":[41],"(1972)":[42],"extended":[43],"Rudolph's":[44],"algorithm":[45],"a":[47,103],"two-step":[48],"correcting":[52],"same":[54,81],"number":[55],"errors":[57],"Reed's":[59],"celebrated":[60],"multi-step":[61],"decoder.":[64],"Here,":[65],"we":[66],"study":[67],"subspace":[71,108],"It":[73],"turns":[74],"out":[75],"these":[77],"have":[79],"capability":[85],"designs,":[91],"but":[92],"their":[93],"complexity":[97,113],"sometimes":[99],"drastically":[100],"improved.":[101],"For":[102],"known":[104],"infinite":[105],"series":[106],"reduction":[111],"exponential.":[115]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
