{"id":"https://openalex.org/W2000492750","doi":"https://doi.org/10.1007/s002000050084","title":"On the Decoding of Cyclic Codes Using Gr\u00f6bner Bases","display_name":"On the Decoding of Cyclic Codes Using Gr\u00f6bner Bases","publication_year":1997,"publication_date":"1997-12-01","ids":{"openalex":"https://openalex.org/W2000492750","doi":"https://doi.org/10.1007/s002000050084","mag":"2000492750"},"language":"en","primary_location":{"id":"doi:10.1007/s002000050084","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002000050084","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","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/A5070959365","display_name":"Philippe Loustaunau","orcid":null},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Philippe Loustaunau","raw_affiliation_strings":["Department of Mathematical Sciences, George Mason University, Fair fax, VA 22030, USA (e-mail: ploust@gmu.edu), , , , , , US","Department of Mathematical Sciences, George Mason University, Fair fax, VA 22030, USA (e-mail: ploust@gmu.edu), , US"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, George Mason University, Fair fax, VA 22030, USA (e-mail: ploust@gmu.edu), , , , , , US","institution_ids":["https://openalex.org/I162714631"]},{"raw_affiliation_string":"Department of Mathematical Sciences, George Mason University, Fair fax, VA 22030, USA (e-mail: ploust@gmu.edu), , US","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090709139","display_name":"E.V. York","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric V. York","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, IN 46556-5683, USA (e-mail: eyork@nd.edu), , , , , , US","Department of Mathematics, University of Notre Dame, IN 46556-5683, USA (e-mail: eyork@nd.edu), US"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, IN 46556-5683, USA (e-mail: eyork@nd.edu), , , , , , US","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, IN 46556-5683, USA (e-mail: eyork@nd.edu), US","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070959365"],"corresponding_institution_ids":["https://openalex.org/I162714631"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.8113,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.86702537,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"6","first_page":"469","last_page":"483"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9965000152587891,"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/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.8614335060119629},{"id":"https://openalex.org/keywords/binary-golay-code","display_name":"Binary Golay code","score":0.7934582829475403},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.7497594952583313},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6661668419837952},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6382156610488892},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6161530017852783},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6043277382850647},{"id":"https://openalex.org/keywords/berlekamp\u2013welch-algorithm","display_name":"Berlekamp\u2013Welch algorithm","score":0.5702757239341736},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5563442707061768},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49892663955688477},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4865385591983795},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.43494102358818054},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43328818678855896},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41831862926483154},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3463653326034546},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.30641111731529236},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28073304891586304},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.18328022956848145},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.14365515112876892},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.13806509971618652},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12915462255477905}],"concepts":[{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.8614335060119629},{"id":"https://openalex.org/C165293857","wikidata":"https://www.wikidata.org/wiki/Q1534522","display_name":"Binary Golay code","level":2,"score":0.7934582829475403},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7497594952583313},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6661668419837952},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6382156610488892},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6161530017852783},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6043277382850647},{"id":"https://openalex.org/C132727834","wikidata":"https://www.wikidata.org/wiki/Q4892328","display_name":"Berlekamp\u2013Welch algorithm","level":5,"score":0.5702757239341736},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5563442707061768},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49892663955688477},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4865385591983795},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.43494102358818054},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43328818678855896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41831862926483154},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3463653326034546},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.30641111731529236},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28073304891586304},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.18328022956848145},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.14365515112876892},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.13806509971618652},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12915462255477905},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s002000050084","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002000050084","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.204.8670","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.204.8670","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.risc.jku.at/research/theorema/Groebner-Bases-Bibliography/gbbib_files/publication_393.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1484535627","https://openalex.org/W1535234872","https://openalex.org/W1594652978","https://openalex.org/W1606480398","https://openalex.org/W1970481743","https://openalex.org/W1986275363","https://openalex.org/W2029622487","https://openalex.org/W2059522106","https://openalex.org/W2071184318","https://openalex.org/W2144253890","https://openalex.org/W2145738710","https://openalex.org/W2153471038","https://openalex.org/W2158558186","https://openalex.org/W2162442687","https://openalex.org/W2171613506","https://openalex.org/W2319466955","https://openalex.org/W2753467868"],"related_works":["https://openalex.org/W2385322349","https://openalex.org/W2369600518","https://openalex.org/W2370284973","https://openalex.org/W2028976748","https://openalex.org/W2050784748","https://openalex.org/W2383267581","https://openalex.org/W2102627024","https://openalex.org/W2182594114","https://openalex.org/W2085052822","https://openalex.org/W2091121840"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}