{"id":"https://openalex.org/W2976785461","doi":"https://doi.org/10.1109/isit.2019.8849850","title":"On Dual Codes in the Doob Schemes","display_name":"On Dual Codes in the Doob Schemes","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2976785461","doi":"https://doi.org/10.1109/isit.2019.8849850","mag":"2976785461"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849850","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","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/A5060058800","display_name":"Denis S. Krotov","orcid":"https://orcid.org/0000-0002-8516-755X"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Denis S. Krotov","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia","Sobolev Institute of Mathematics, Novosibirsk, Russia"],"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060058800"],"corresponding_institution_ids":["https://openalex.org/I4210096862"],"apc_list":null,"apc_paid":null,"fwci":0.1447,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58556437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1917","last_page":"1921"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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/T10849","display_name":"Finite Group Theory Research","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33157509565353394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29919537901878357}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33157509565353394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29919537901878357}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2019.8849850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849850","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","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":10,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1975339667","https://openalex.org/W2008192074","https://openalex.org/W2010238614","https://openalex.org/W2053175045","https://openalex.org/W2167413626","https://openalex.org/W3099948922","https://openalex.org/W3102043406","https://openalex.org/W4214772016","https://openalex.org/W6785772411"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542"],"abstract_inverted_index":{"The":[0],"Doob":[1,124],"scheme":[2,11,125,192],"D(m,":[3,126],"n'":[4,127],"+":[5],"n'')":[6],"is":[7,129],"a":[8,86,158],"metric":[9],"association":[10],"defined":[12],"on":[13,51,104],"E":[14,39,163],"<sub":[15,23,31,40,53,61,69,164,172],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16,19,24,27,32,35,41,46,54,57,62,65,70,73,145,165,168,173,176,187],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4</sub>":[17,25,33,42,55,71,166,174],"<sup":[18,26,34,45,56,64,72,144,167,175,186],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[20,169],"X":[21,29,59,67,170],"F":[22,171],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n'</sup>":[28,177],"Z":[30,52,60,68],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n''</sup>":[36,74],",":[37,178],"where":[38],"=":[43],"GR(4":[44],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[47],")":[48],"or,":[49],"alternatively,":[50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2m</sup>":[58],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[63],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2n'</sup>":[66],".":[75],"We":[76,151],"prove":[77],"the":[78,82,101,105,114,123,132,136,140,148,155,179,190],"MacWilliams":[79,133],"identities":[80,134],"connecting":[81],"weight":[83,115,137,180],"distributions":[84,181],"of":[85,117,139,157,182],"linear":[87,159],"or":[88],"additive":[89,119],"code":[90,120,142,160],"and":[91,184],"its":[92],"dual.":[93],"In":[94],"particular,":[95],"for":[96],"each":[97],"case,":[98],"we":[99],"determine":[100],"dual":[102,141,149],"scheme,":[103],"same":[106,191],"set":[107],"but":[108],"with":[109,135],"different":[110],"metric,":[111],"such":[112],"that":[113,153],"distribution":[116,138],"an":[118],"C":[121,143,161,183,185],"in":[122,147,154,162,189],"+n'')":[128],"related":[130],"by":[131],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u22a5</sup>":[146,188],"scheme.":[150],"note":[152],"case":[156],"are":[193],"also":[194],"connected.":[195]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}