{"id":"https://openalex.org/W2010604914","doi":"https://doi.org/10.1109/cig.2010.5592677","title":"The Euclidean algorithm for Generalized Minimum Distance decoding of Reed-Solomon codes","display_name":"The Euclidean algorithm for Generalized Minimum Distance decoding of Reed-Solomon codes","publication_year":2010,"publication_date":"2010-08-01","ids":{"openalex":"https://openalex.org/W2010604914","doi":"https://doi.org/10.1109/cig.2010.5592677","mag":"2010604914"},"language":"en","primary_location":{"id":"doi:10.1109/cig.2010.5592677","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cig.2010.5592677","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Information Theory Workshop","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1006.2860","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007506114","display_name":"Sabine Kampf","orcid":null},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]},{"id":"https://openalex.org/I90697900","display_name":"EBS University of Business and Law","ror":"https://ror.org/01js9jv94","country_code":"DE","type":"education","lineage":["https://openalex.org/I90697900"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sabine Kampf","raw_affiliation_strings":["Institute of Telecommunications and Applied Information Theory, University of Ulm (EBS), Germany","Institute of Telecommunications and Applied Information Theory, University of Ulm, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Telecommunications and Applied Information Theory, University of Ulm (EBS), Germany","institution_ids":["https://openalex.org/I90697900","https://openalex.org/I196349391"]},{"raw_affiliation_string":"Institute of Telecommunications and Applied Information Theory, University of Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045353828","display_name":"Martin Bossert","orcid":"https://orcid.org/0000-0002-3827-9065"},"institutions":[{"id":"https://openalex.org/I90697900","display_name":"EBS University of Business and Law","ror":"https://ror.org/01js9jv94","country_code":"DE","type":"education","lineage":["https://openalex.org/I90697900"]},{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Bossert","raw_affiliation_strings":["Institute of Telecommunications and Applied Information Theory, University of Ulm (EBS), Germany","Institute of Telecommunications and Applied Information Theory, University of Ulm, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Telecommunications and Applied Information Theory, University of Ulm (EBS), Germany","institution_ids":["https://openalex.org/I90697900","https://openalex.org/I196349391"]},{"raw_affiliation_string":"Institute of Telecommunications and Applied Information Theory, University of Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007506114"],"corresponding_institution_ids":["https://openalex.org/I196349391","https://openalex.org/I90697900"],"apc_list":null,"apc_paid":null,"fwci":1.8619,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.87245039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9977999925613403,"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":0.9970999956130981,"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/euclidean-algorithm","display_name":"Euclidean algorithm","score":0.8153007626533508},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.81004798412323},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.7904701232910156},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.7199835181236267},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.6545411348342896},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.6502610445022583},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.57157301902771},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5622609853744507},{"id":"https://openalex.org/keywords/reed\u2013solomon-error-correction","display_name":"Reed\u2013Solomon error correction","score":0.4751396179199219},{"id":"https://openalex.org/keywords/berlekamp\u2013welch-algorithm","display_name":"Berlekamp\u2013Welch algorithm","score":0.472308874130249},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44483041763305664},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.4127638339996338},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40404969453811646},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36660945415496826},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3404434323310852},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.3262420892715454},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.26647302508354187},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14382007718086243},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.11410093307495117}],"concepts":[{"id":"https://openalex.org/C98371066","wikidata":"https://www.wikidata.org/wiki/Q230848","display_name":"Euclidean algorithm","level":2,"score":0.8153007626533508},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.81004798412323},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.7904701232910156},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.7199835181236267},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.6545411348342896},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.6502610445022583},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.57157301902771},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5622609853744507},{"id":"https://openalex.org/C78065487","wikidata":"https://www.wikidata.org/wiki/Q1061598","display_name":"Reed\u2013Solomon error correction","level":5,"score":0.4751396179199219},{"id":"https://openalex.org/C132727834","wikidata":"https://www.wikidata.org/wiki/Q4892328","display_name":"Berlekamp\u2013Welch algorithm","level":5,"score":0.472308874130249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44483041763305664},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.4127638339996338},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40404969453811646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36660945415496826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3404434323310852},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.3262420892715454},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.26647302508354187},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14382007718086243},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.11410093307495117},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cig.2010.5592677","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cig.2010.5592677","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Information Theory Workshop","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1006.2860","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1006.2860","pdf_url":"https://arxiv.org/pdf/1006.2860","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.748.8884","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.748.8884","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1006.2860.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1006.2860","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1006.2860","pdf_url":"https://arxiv.org/pdf/1006.2860","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1586790543","https://openalex.org/W1606480398","https://openalex.org/W2016833807","https://openalex.org/W2091697266","https://openalex.org/W2138779125","https://openalex.org/W2155020285","https://openalex.org/W3103004745","https://openalex.org/W3149478760","https://openalex.org/W6635072419"],"related_works":["https://openalex.org/W2952710341","https://openalex.org/W1975709480","https://openalex.org/W2066795426","https://openalex.org/W1548705449","https://openalex.org/W2247418595","https://openalex.org/W2050784748","https://openalex.org/W2541661803","https://openalex.org/W2149639327","https://openalex.org/W2153697125","https://openalex.org/W2146033694"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,45],"method":[4],"to":[5,34],"merge":[6],"Generalized":[7,28],"Minimum":[8,29],"Distance":[9,30],"decoding":[10,31],"of":[11,36,47],"Reed-Solomon":[12],"codes":[13],"with":[14],"the":[15,24,37],"extended":[16,38],"Euclidean":[17,39],"algorithm.":[18,40],"By":[19],"merge,":[20],"we":[21],"mean":[22],"that":[23],"steps":[25],"performed":[26],"in":[27],"are":[32],"similar":[33],"those":[35],"The":[41],"resulting":[42],"algorithm":[43],"has":[44],"complexity":[46],"O(n":[48],"<sup":[49],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[51],").":[52]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
