{"id":"https://openalex.org/W2023063824","doi":"https://doi.org/10.1109/isita.2010.5649516","title":"Unified system of encoding and decoding erasures and errors for algebraic geometry codes","display_name":"Unified system of encoding and decoding erasures and errors for algebraic geometry codes","publication_year":2010,"publication_date":"2010-10-01","ids":{"openalex":"https://openalex.org/W2023063824","doi":"https://doi.org/10.1109/isita.2010.5649516","mag":"2023063824"},"language":"en","primary_location":{"id":"doi:10.1109/isita.2010.5649516","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isita.2010.5649516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 International Symposium On Information Theory & Its Applications","raw_type":"proceedings-article"},"type":"conference-paper","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/A5006877645","display_name":"Hajime Matsui","orcid":"https://orcid.org/0000-0003-4778-8045"},"institutions":[{"id":"https://openalex.org/I4840577","display_name":"Toyota Technological Institute","ror":"https://ror.org/001hv0k59","country_code":"JP","type":"education","lineage":["https://openalex.org/I4840577"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hajime Matsui","raw_affiliation_strings":["Department of Electronics and Information Science, Toyota Technological Institute, Nagoya, Japan","Dept. of Electronics and Information Science, Toyota Technological Institute, Hisakata 2-12-1, Tenpaku, Nagoya 468-8511, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Information Science, Toyota Technological Institute, Nagoya, Japan","institution_ids":["https://openalex.org/I4840577"]},{"raw_affiliation_string":"Dept. of Electronics and Information Science, Toyota Technological Institute, Hisakata 2-12-1, Tenpaku, Nagoya 468-8511, Japan","institution_ids":["https://openalex.org/I4840577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006877645"],"corresponding_institution_ids":["https://openalex.org/I4840577"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.13741029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1001","last_page":"1006"},"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":0.9970999956130981,"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"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9961000084877014,"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/lemma","display_name":"Lemma (botany)","score":0.6352202296257019},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5909196138381958},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.558148980140686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5376222729682922},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.48737698793411255},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.46012258529663086},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.44295674562454224},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43376970291137695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3924989700317383},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3333192467689514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31366586685180664},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19615542888641357}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6352202296257019},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5909196138381958},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.558148980140686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5376222729682922},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.48737698793411255},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.46012258529663086},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.44295674562454224},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43376970291137695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3924989700317383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3333192467689514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31366586685180664},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19615542888641357},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"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:10.1109/isita.2010.5649516","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isita.2010.5649516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 International Symposium On Information Theory & Its Applications","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1557415002","https://openalex.org/W2080290915","https://openalex.org/W2093877555","https://openalex.org/W2097821905","https://openalex.org/W2112639232","https://openalex.org/W2132850797","https://openalex.org/W2158688390","https://openalex.org/W2168932040","https://openalex.org/W2169799190","https://openalex.org/W2247464128","https://openalex.org/W6670588621","https://openalex.org/W6691371516"],"related_works":["https://openalex.org/W2072016134","https://openalex.org/W2351168932","https://openalex.org/W2465690287","https://openalex.org/W2108143034","https://openalex.org/W2376389741","https://openalex.org/W1997850251","https://openalex.org/W2084549431","https://openalex.org/W2115811863","https://openalex.org/W1848880869","https://openalex.org/W1568966867"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"fundamental":[4],"lemma":[5,32,83],"in":[6,16,63,92],"algebraic":[7,22,28,93],"coding":[8],"theory":[9],"is":[10,13,46,61],"established,":[11],"which":[12],"frequently":[14],"appeared":[15],"the":[17,44,49,59,82,104],"encoding":[18,88],"and":[19,27,43,57,75,89],"decoding":[20,90],"for":[21,103],"codes":[23],"such":[24],"as":[25],"Reed-Solomon":[26],"geometry":[29,94],"codes.":[30,95],"This":[31],"states":[33],"that":[34],"two":[35],"vector":[36],"spaces,":[37],"one":[38],"corresponds":[39],"to":[40,84],"information":[41],"symbols":[42],"other":[45],"indexed":[47],"by":[48,67],"support":[50],"of":[51,65,87],"Gr\u00f6bner":[52,73],"basis,":[53],"are":[54],"canonically":[55],"isomorphic,":[56],"moreover,":[58],"isomorphism":[60],"given":[62],"terms":[64],"extension":[66],"linear":[68],"feedback":[69],"shift":[70],"registers":[71],"from":[72],"basis":[74],"discrete":[76],"Fourier":[77],"transforms.":[78],"Next,":[79],"we":[80,97],"apply":[81],"unified":[85],"system":[86],"erasure-errors":[91],"Finally,":[96],"comment":[98],"on":[99],"an":[100],"improved":[101],"bound":[102],"generic":[105],"erasure-error":[106],"correcting":[107],"capabilities.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}