{"id":"https://openalex.org/W2160997819","doi":"https://doi.org/10.1109/tit.2011.2162173","title":"Linearized Shift-Register Synthesis","display_name":"Linearized Shift-Register Synthesis","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W2160997819","doi":"https://doi.org/10.1109/tit.2011.2162173","mag":"2160997819"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2162173","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162173","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072164594","display_name":"Vladimir Sidorenko","orcid":"https://orcid.org/0000-0003-4966-3684"},"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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Vladimir Sidorenko","raw_affiliation_strings":["IITP, Russian Academy of Science, Moscow, Russia","Institute of Telecommunications and Applied Information Theory, TAIT, Ulm University, Ulm, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IITP, Russian Academy of Science, Moscow, Russia","institution_ids":[]},{"raw_affiliation_string":"Institute of Telecommunications and Applied Information Theory, TAIT, Ulm University, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060531157","display_name":"G. Richter","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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerd Richter","raw_affiliation_strings":["Institute of Telecommunications and Applied Information Theory, TAIT, Ulm University, Ulm, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Telecommunications and Applied Information Theory, TAIT, Ulm University, 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/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, TAIT, Ulm University, Ulm, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Telecommunications and Applied Information Theory, TAIT, Ulm University, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I196349391"],"apc_list":null,"apc_paid":null,"fwci":4.3963,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94665441,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"57","issue":"9","first_page":"6025","last_page":"6032"},"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":0.9983999729156494,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9961000084877014,"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/algorithm","display_name":"Algorithm","score":0.4489431381225586},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.4404626786708832},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43741416931152344},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3478325605392456}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4489431381225586},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.4404626786708832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43741416931152344},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3478325605392456}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2011.2162173","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2162173","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320325530","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1520973602","https://openalex.org/W1531894771","https://openalex.org/W1593639131","https://openalex.org/W1593683169","https://openalex.org/W1594652978","https://openalex.org/W1969206571","https://openalex.org/W1993359877","https://openalex.org/W1997244826","https://openalex.org/W2016833807","https://openalex.org/W2055060019","https://openalex.org/W2057174629","https://openalex.org/W2095547380","https://openalex.org/W2100556391","https://openalex.org/W2115216868","https://openalex.org/W2139416652","https://openalex.org/W2158558186","https://openalex.org/W2159047322","https://openalex.org/W2162442687","https://openalex.org/W2613956024","https://openalex.org/W3151140615","https://openalex.org/W4285719527","https://openalex.org/W6631960143","https://openalex.org/W6635485285"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W3008339103","https://openalex.org/W2404647514","https://openalex.org/W1667647204","https://openalex.org/W4247536566","https://openalex.org/W3119814709","https://openalex.org/W2018477250","https://openalex.org/W1508895727","https://openalex.org/W4241418540","https://openalex.org/W2725786787"],"abstract_inverted_index":{"An":[0],"efficient":[1],"algorithm":[2,87],"synthesizing":[3],"all":[4],"shortest":[5],"<i":[6,17,25,48,52,57,61,71,76],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,18,26,49,53,58,62,65,72,77],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</i>":[8],"-linearized-feedback":[9],"shift-registers":[10],"generating":[11],"a":[12,21,39],"given":[13],"sequence":[14],"of":[15,41,83],"length":[16],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>":[19,63],"over":[20],"finite":[22],"field":[23],"\\BBF":[24,70],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">qm</i>":[27,73],"is":[28,33,38,79],"derived":[29],"and":[30],"its":[31],"correctness":[32],"proved.":[34],"This":[35],"algorithm,":[36,44],"which":[37],"generalization":[40],"the":[42,80,84,94],"Berlekamp-Massey":[43],"has":[45],"time":[46],"complexity":[47,82],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">O</i>":[50,59],"(":[51,60],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">lN</i>":[54],")":[55,67],"<;~":[56],"<sup":[64],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[66],"operations":[68],"in":[69],",":[74],"where":[75],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[78],"linearized":[81],"sequence.":[85],"The":[86],"can":[88],"be":[89],"applied":[90],"for":[91],"efficiently":[92],"solving":[93],"key":[95],"equation":[96],"when":[97],"decoding":[98],"Gabidulin":[99],"codes.":[100]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
