{"id":"https://openalex.org/W2345387074","doi":"https://doi.org/10.3934/amc.2016015","title":"On the error distance of extended Reed-Solomon codes","display_name":"On the error distance of extended Reed-Solomon codes","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2345387074","doi":"https://doi.org/10.3934/amc.2016015","mag":"2345387074"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2016015","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016015","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2016015","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081416508","display_name":"YuJuan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yujuan Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036016784","display_name":"Guizhen Zhu","orcid":"https://orcid.org/0000-0003-4166-4316"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guizhen Zhu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081416508"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1104,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.9287706,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"10","issue":"2","first_page":"413","last_page":"427"},"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":0.9973000288009644,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reed\u2013solomon-error-correction","display_name":"Reed\u2013Solomon error correction","score":0.9261689186096191},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8225964307785034},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6913830041885376},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.5577276945114136},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5094624161720276},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.5058826804161072},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.491345077753067},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.4680357277393341},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.4515511095523834},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.41686806082725525},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.39933231472969055},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3740716576576233},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3618960380554199},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35452190041542053},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.26179492473602295},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25399670004844666},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.056102454662323}],"concepts":[{"id":"https://openalex.org/C78065487","wikidata":"https://www.wikidata.org/wiki/Q1061598","display_name":"Reed\u2013Solomon error correction","level":5,"score":0.9261689186096191},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8225964307785034},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6913830041885376},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.5577276945114136},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5094624161720276},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.5058826804161072},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.491345077753067},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.4680357277393341},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.4515511095523834},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.41686806082725525},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.39933231472969055},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3740716576576233},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3618960380554199},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35452190041542053},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.26179492473602295},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25399670004844666},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.056102454662323},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2016015","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016015","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2016015","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016015","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W107280146","https://openalex.org/W1483729734","https://openalex.org/W1500755669","https://openalex.org/W1539963681","https://openalex.org/W1565759886","https://openalex.org/W1598407298","https://openalex.org/W1816551856","https://openalex.org/W2032431003","https://openalex.org/W2046947513","https://openalex.org/W2053340927","https://openalex.org/W2057886417","https://openalex.org/W2077712820","https://openalex.org/W2089272132","https://openalex.org/W2103236224","https://openalex.org/W2110614437","https://openalex.org/W2174870427","https://openalex.org/W2613956024","https://openalex.org/W2950077823","https://openalex.org/W2969595239","https://openalex.org/W3020932339"],"related_works":["https://openalex.org/W2157055070","https://openalex.org/W2083307409","https://openalex.org/W2247418595","https://openalex.org/W2146067565","https://openalex.org/W1798117689","https://openalex.org/W2121777163","https://openalex.org/W1976052006","https://openalex.org/W2625239423","https://openalex.org/W4285494694","https://openalex.org/W2133789648"],"abstract_inverted_index":{"It":[0],"is":[1,14],"well":[2],"known":[3],"that":[4],"the":[5,10,16,31,43,54,59],"main":[6],"problem":[7,62],"of":[8,19,34,56,63],"decoding":[9],"extended":[11,44],"Reed-Solomon":[12,45,64],"codes":[13],"computing":[15],"error":[17,32],"distance":[18,33],"a":[20,48],"word.":[21],"Using":[22],"some":[23],"algebraic":[24],"constructions,":[25],"we":[26,50],"are":[27,38],"able":[28],"to":[29,42],"determine":[30],"words":[35],"whose":[36],"degrees":[37],"$k+1$":[39],"and":[40],"$k+2$":[41],"codes.":[46,65],"As":[47],"corollary,":[49],"can":[51],"simply":[52],"get":[53],"results":[55],"Zhang-Fu-Liao":[57],"on":[58],"deep":[60],"hole":[61]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}