{"id":"https://openalex.org/W2101303074","doi":"https://doi.org/10.1109/itw.2005.1531889","title":"On polyalphabetic block codes","display_name":"On polyalphabetic block codes","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2101303074","doi":"https://doi.org/10.1109/itw.2005.1531889","mag":"2101303074"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2005.1531889","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2005.1531889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Information Theory Workshop, 2005.","raw_type":"proceedings-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":true,"raw_author_name":"V. Sidorenko","raw_affiliation_strings":["Department of Telecommunications and Applied Information Theory, University of Ulm (EBS), Ulm, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Telecommunications and Applied Information Theory, University of Ulm (EBS), Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031644344","display_name":"G. Schmidt","orcid":"https://orcid.org/0000-0001-6852-7560"},"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":"G. Schmidt","raw_affiliation_strings":["Department of Telecommunications and Applied Information Theory, University of Ulm (EBS), Ulm, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Telecommunications and Applied Information Theory, University of Ulm (EBS), Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058481417","display_name":"E.M. Gabidulin","orcid":null},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"E. Gabidulin","raw_affiliation_strings":["Moscow Institute of Physics and Technology, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Moscow, Russia","institution_ids":["https://openalex.org/I153845743"]}]},{"author_position":"middle","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":"M. Bossert","raw_affiliation_strings":["Department of Telecommunications and Applied Information Theory, University of Ulm (EBS), Ulm, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Telecommunications and Applied Information Theory, University of Ulm (EBS), Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111884365","display_name":"Valentin Afanassiev","orcid":null},"institutions":[{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"V. Afanassiev","raw_affiliation_strings":["Institute for Information Transmission Problems, Russian Academy of Science, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Institute for Information Transmission Problems, Russian Academy of Science, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5072164594"],"corresponding_institution_ids":["https://openalex.org/I196349391"],"apc_list":null,"apc_paid":null,"fwci":0.9134,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81540941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"4 pp.","last_page":"4 pp."},"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":0.9998000264167786,"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/T10796","display_name":"Cooperative Communication and Network Coding","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/block-code","display_name":"Block code","score":0.7007894515991211},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.6142441630363464},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.6008262038230896},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.56742262840271},{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.5561662912368774},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.49048492312431335},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.48787736892700195},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4823529124259949},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.482075035572052},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4612983167171478},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46067628264427185},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.4583034813404083},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.44997721910476685},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.44600313901901245},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4427301585674286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42376866936683655},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.41880345344543457},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.41799747943878174},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.39472854137420654},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29074206948280334}],"concepts":[{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.7007894515991211},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6142441630363464},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.6008262038230896},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.56742262840271},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.5561662912368774},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.49048492312431335},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.48787736892700195},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4823529124259949},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.482075035572052},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4612983167171478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46067628264427185},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.4583034813404083},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.44997721910476685},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.44600313901901245},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4427301585674286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42376866936683655},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.41880345344543457},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.41799747943878174},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.39472854137420654},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29074206948280334},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itw.2005.1531889","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2005.1531889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Information Theory Workshop, 2005.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1581232847","https://openalex.org/W1606480398","https://openalex.org/W2032431003","https://openalex.org/W2074888732","https://openalex.org/W2098081605","https://openalex.org/W2151987797","https://openalex.org/W2165062870","https://openalex.org/W4210992409"],"related_works":["https://openalex.org/W2943247777","https://openalex.org/W2361015587","https://openalex.org/W2121408388","https://openalex.org/W2740543340","https://openalex.org/W4302175014","https://openalex.org/W2045996052","https://openalex.org/W2952823298","https://openalex.org/W2149558777","https://openalex.org/W3176812878","https://openalex.org/W4287640798"],"abstract_inverted_index":{"A":[0],"polyalphabetic":[1,58,69,82],"(or":[2],"mixed)":[3],"block":[4],"code":[5,59],"is":[6],"a":[7,18,32,57],"set":[8],"of":[9,11,17,43,56,68,80],"codewords":[10],"finite":[12],"length,":[13],"where":[14,35],"every":[15],"symbol":[16],"codeword":[19],"belongs":[20],"to":[21,27],"its":[22],"own":[23],"alphabet.":[24],"In":[25],"contrast":[26],"previous":[28],"publications":[29],"we":[30,36],"consider":[31],"general":[33],"case,":[34],"do":[37],"not":[38],"assume":[39],"any":[40],"algebraic":[41],"structure":[42],"the":[44,47,54,81,97,108],"alphabets":[45],"and":[46,50,78,93],"codes.":[48,76],"Upper":[49],"lower":[51],"bounds":[52],"on":[53,74],"cardinality":[55],"with":[60],"given":[61],"Hamming":[62],"distance":[63],"are":[64,71,104],"obtained.":[65],"Some":[66],"constructions":[67],"codes":[70,103],"suggested":[72],"based":[73],"known":[75],"Encoding":[77],"decoding":[79,94],"codes,":[83],"obtained":[84],"in":[85],"this":[86,101],"way,":[87],"can":[88],"be":[89],"done":[90],"using":[91],"encoding":[92],"algorithms":[95],"for":[96],"mother":[98],"code.":[99],"Using":[100],"constructions,":[102],"obtained,":[105],"that":[106],"reach":[107],"upper":[109],"Singleton":[110],"type":[111],"bound.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-02T13:48:15.688549","created_date":"2025-10-10T00:00:00"}