{"id":"https://openalex.org/W3197995420","doi":"https://doi.org/10.1109/isit45174.2021.9517971","title":"Distance Enumerators for Number-Theoretic Codes","display_name":"Distance Enumerators for Number-Theoretic Codes","publication_year":2021,"publication_date":"2021-07-12","ids":{"openalex":"https://openalex.org/W3197995420","doi":"https://doi.org/10.1109/isit45174.2021.9517971","mag":"3197995420"},"language":"en","primary_location":{"id":"doi:10.1109/isit45174.2021.9517971","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517971","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 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/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":["Yamaguchi University,JAPAN","Yamaguchi University, JAPAN"],"affiliations":[{"raw_affiliation_string":"Yamaguchi University,JAPAN","institution_ids":["https://openalex.org/I173915773"]},{"raw_affiliation_string":"Yamaguchi University, 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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08438268,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"308","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":1.0,"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":1.0,"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":0.9987999796867371,"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/T10207","display_name":"Advanced biosensing and bioanalysis techniques","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.7180323004722595},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.6212025284767151},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5694748163223267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.55134516954422},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4873226583003998},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.45479798316955566},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4530574381351471},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4411434531211853},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.4359261393547058},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.4282502233982086},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3604910373687744},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3400658071041107},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.322053998708725}],"concepts":[{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.7180323004722595},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6212025284767151},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5694748163223267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.55134516954422},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4873226583003998},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.45479798316955566},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4530574381351471},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4411434531211853},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.4359261393547058},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4282502233982086},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3604910373687744},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3400658071041107},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.322053998708725},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"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/isit45174.2021.9517971","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517971","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 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":17,"referenced_works":["https://openalex.org/W1538132246","https://openalex.org/W1647671624","https://openalex.org/W2036600344","https://openalex.org/W2081354249","https://openalex.org/W2108763551","https://openalex.org/W2160103937","https://openalex.org/W2163962630","https://openalex.org/W2584151571","https://openalex.org/W2887852579","https://openalex.org/W2889486395","https://openalex.org/W2903840876","https://openalex.org/W2963561675","https://openalex.org/W2975111200","https://openalex.org/W3081509103","https://openalex.org/W3112383012","https://openalex.org/W6636915900","https://openalex.org/W6754623748"],"related_works":["https://openalex.org/W1969401961","https://openalex.org/W1541021634","https://openalex.org/W2048794010","https://openalex.org/W2135232882","https://openalex.org/W4302771537","https://openalex.org/W4285078748","https://openalex.org/W2364890299","https://openalex.org/W2058919686","https://openalex.org/W2562336992","https://openalex.org/W2125814644"],"abstract_inverted_index":{"The":[0,41,71],"number-theoretic":[1,26,95],"codes":[2,7,27,36],"are":[3,15,28],"a":[4,45,48],"class":[5],"of":[6,44,60,63,81,89],"defined":[8],"by":[9],"single":[10],"or":[11],"multiple":[12],"congruences":[13],"and":[14,21],"mainly":[16],"used":[17],"for":[18,34,93,107],"correcting":[19],"insertion":[20],"deletion":[22],"errors.":[23],"Since":[24],"the":[25,31,58,61,75,82,90,94,103,108],"generally":[29],"non-linear,":[30],"analysis":[32],"method":[33],"such":[35],"is":[37,47],"not":[38],"established":[39],"enough.":[40],"distance":[42,66,72,91,105],"enumerator":[43,73,106],"code":[46],"unary":[49],"polynomial":[50],"whose":[51],"<tex":[52,67],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[53,68],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$i$</tex>":[54,69],"th":[55],"coefficient":[56],"gives":[57,74],"number":[59],"pairs":[62],"codewords":[64],"with":[65],".":[70],"maximum":[76],"likelihood":[77],"decoding":[78],"error":[79],"probability":[80],"code.":[83],"This":[84],"paper":[85],"presents":[86],"an":[87,99],"identity":[88],"enumerators":[92],"codes.":[96,111],"Moreover,":[97],"as":[98],"example,":[100],"we":[101],"derive":[102],"Hamming":[104],"Varshamov-Tenengolts":[109],"(VT)":[110]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
