{"id":"https://openalex.org/W3217795677","doi":"https://doi.org/10.1109/tit.2022.3184776","title":"Weight Enumerators and Cardinalities for Number-Theoretic Codes","display_name":"Weight Enumerators and Cardinalities for Number-Theoretic Codes","publication_year":2022,"publication_date":"2022-06-21","ids":{"openalex":"https://openalex.org/W3217795677","doi":"https://doi.org/10.1109/tit.2022.3184776","mag":"3217795677"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3184776","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3184776","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.05787","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011452126","display_name":"T. Nozaki","orcid":"https://orcid.org/0000-0003-3102-5764"},"institutions":[{"id":"https://openalex.org/I173915773","display_name":"Yamaguchi University","ror":"https://ror.org/03cxys317","country_code":"JP","type":"education","lineage":["https://openalex.org/I173915773"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Takayuki Nozaki","raw_affiliation_strings":["Department of Informatics, Yamaguchi University, Yamaguchi, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Yamaguchi University, Yamaguchi, Japan","institution_ids":["https://openalex.org/I173915773"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011452126"],"corresponding_institution_ids":["https://openalex.org/I173915773"],"apc_list":null,"apc_paid":null,"fwci":0.0867,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.39737627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"68","issue":"11","first_page":"7165","last_page":"7173"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10207","display_name":"Advanced biosensing and bioanalysis techniques","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9979000091552734,"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/hamming-code","display_name":"Hamming code","score":0.789259672164917},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7423425912857056},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6328176856040955},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6147463917732239},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.5982383489608765},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.57826167345047},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5449250936508179},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5003681182861328},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.477622926235199},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4618021845817566},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.44093188643455505},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.42510756850242615},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.204130619764328},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.16069170832633972},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1573568880558014}],"concepts":[{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.789259672164917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7423425912857056},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6328176856040955},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6147463917732239},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.5982383489608765},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.57826167345047},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5449250936508179},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5003681182861328},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.477622926235199},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4618021845817566},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.44093188643455505},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.42510756850242615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.204130619764328},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.16069170832633972},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1573568880558014},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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":2,"locations":[{"id":"doi:10.1109/tit.2022.3184776","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3184776","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"},{"id":"pmh:oai:arXiv.org:2001.05787","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.05787","pdf_url":"https://arxiv.org/pdf/2001.05787","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.05787","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.05787","pdf_url":"https://arxiv.org/pdf/2001.05787","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3770224511","display_name":null,"funder_award_id":"22K11905","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W181127821","https://openalex.org/W1538132246","https://openalex.org/W1594346180","https://openalex.org/W1606480398","https://openalex.org/W1647671624","https://openalex.org/W1995728465","https://openalex.org/W2015385212","https://openalex.org/W2081354249","https://openalex.org/W2108763551","https://openalex.org/W2132619738","https://openalex.org/W2517317591","https://openalex.org/W2584151571","https://openalex.org/W2597746962","https://openalex.org/W2798946892","https://openalex.org/W2887852579","https://openalex.org/W2889486395","https://openalex.org/W2889940767","https://openalex.org/W2963284721","https://openalex.org/W2963969457","https://openalex.org/W2975111200","https://openalex.org/W3033119398","https://openalex.org/W3081509103","https://openalex.org/W3106364761","https://openalex.org/W3112383012","https://openalex.org/W6607364932","https://openalex.org/W6632141683","https://openalex.org/W6636915900","https://openalex.org/W6735058501","https://openalex.org/W6754623748","https://openalex.org/W6787260699"],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2105471374","https://openalex.org/W2963549154","https://openalex.org/W2158117886","https://openalex.org/W1987803429","https://openalex.org/W2963553930","https://openalex.org/W4295308639","https://openalex.org/W2064682118","https://openalex.org/W2376984781","https://openalex.org/W1793009983"],"abstract_inverted_index":{"The":[0],"number-theoretic":[1,45,60],"code":[2],"is":[3],"a":[4,33,36,63],"class":[5],"of":[6,38,75,102],"codes":[7,15,98],"defined":[8],"by":[9],"single":[10,81],"or":[11,83],"multiple":[12],"congruences.":[13],"These":[14],"are":[16],"mainly":[17],"used":[18],"for":[19,26,35,43,58,95],"correcting":[20,27,80],"insertion":[21,82],"and":[22,25,56,73],"deletion":[23],"errors,":[24],"asymmetric":[28],"errors.":[29],"This":[30,47],"paper":[31,67],"presents":[32],"formula":[34,48,90],"generalization":[37],"the":[39,44,53,59,69,76,89,92,96,100],"complete":[40],"weight":[41,54,71],"enumerator":[42],"codes.":[46,61],"allows":[49],"us":[50],"to":[51],"derive":[52],"enumerators":[55,72],"cardinalities":[57,74],"As":[62],"special":[64],"case,":[65],"this":[66],"provides":[68],"Hamming":[70],"non-binary":[77],"Tenengolts\u2019":[78],"codes,":[79],"deletion.":[84],"Moreover,":[85],"we":[86],"show":[87],"that":[88],"deduces":[91],"MacWilliams":[93],"identity":[94],"linear":[97],"over":[99],"ring":[101],"integers":[103],"modulo":[104],"<inline-formula":[105],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[106],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[107],"<tex-math":[108],"notation=\"LaTeX\">$r$":[109],"</tex-math></inline-formula>":[110],".":[111]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}