{"id":"https://openalex.org/W2889940767","doi":"https://doi.org/10.1109/tit.2018.2883759","title":"On $Z_p Z_{p^k}$ -Additive Codes and Their Duality","display_name":"On $Z_p Z_{p^k}$ -Additive Codes and Their Duality","publication_year":2018,"publication_date":"2018-11-30","ids":{"openalex":"https://openalex.org/W2889940767","doi":"https://doi.org/10.1109/tit.2018.2883759","mag":"2889940767"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2883759","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/1809.00008","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044196416","display_name":"Minjia Shi","orcid":"https://orcid.org/0000-0002-4990-6271"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"funder","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Minjia Shi","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072352158","display_name":"Rongsheng Wu","orcid":"https://orcid.org/0000-0002-2361-5126"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"funder","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rongsheng Wu","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","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":"funder","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Denis S. Krotov","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia"],"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.569,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":16,"citation_normalized_percentile":{"value":0.867018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":89},"biblio":{"volume":"65","issue":"6","first_page":"3841","last_page":"3847"},"is_retracted":false,"is_paratext":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":0.9967,"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":0.9925,"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":[],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32181895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20169356}],"mesh":[],"locations_count":4,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2883759","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.00008","pdf_url":"http://arxiv.org/pdf/1809.00008","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1809.00008","pdf_url":"https://arxiv.org/pdf/1809.00008","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.1809.00008","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.00008","pdf_url":"http://arxiv.org/pdf/1809.00008","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China","award_id":"61672036"},{"funder":"https://openalex.org/F4320334801","funder_display_name":"Russian Academy of Sciences","award_id":"0314-2016-0016"},{"funder":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province","award_id":"1808085J20"}],"datasets":[],"versions":["https://openalex.org/W2889940767","https://openalex.org/W3106364761"],"referenced_works_count":17,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1604526698","https://openalex.org/W1606480398","https://openalex.org/W1987121126","https://openalex.org/W2010238614","https://openalex.org/W2010825458","https://openalex.org/W2015797376","https://openalex.org/W2038681062","https://openalex.org/W2045545810","https://openalex.org/W2046471908","https://openalex.org/W2109887866","https://openalex.org/W2117013900","https://openalex.org/W2121513675","https://openalex.org/W2317616482","https://openalex.org/W2397670217","https://openalex.org/W2560132596","https://openalex.org/W2892003982"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3212023493","https://openalex.org/W3103304230","https://openalex.org/W2980963558","https://openalex.org/W2572370460","https://openalex.org/W2185360082","https://openalex.org/W2090715877","https://openalex.org/W1992365905","https://openalex.org/W1976691234","https://openalex.org/W1882246857"],"abstract_inverted_index":{"In":[0,151],"this":[1],"paper,":[2],"two":[3,69],"different":[4],"Gray-like":[5],"maps":[6],"from":[7],"Z":[8,16,29,78,82,125,162,166,174],"p":[11,32,81,85,165,169,177],"\u03b1":[14],"\u00d7":[15],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">pk":[19],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b2":[22],",":[23,36,45],"where":[24],"p":[25,147],"is":[26,76,93,116,142,180],"prime,":[27],"to":[28,144],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n":[35],"n":[37],"=":[38],"\u03b1":[39],"t":[40],"\u03b2p":[41],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k-1":[44],"denoted":[46],"by":[47],"\u03c6":[48],"and":[49,88,106,139,148],"\u03a6,":[50],"respectively,":[51],"are":[52,112],"presented.":[53],"We":[54,71],"have":[55],"determined":[56],"the":[57,60,64,97,101,140,160],"connection":[58],"between":[59],"weight":[61,98],"enumerators":[62,99],"among":[63],"image":[65,102],"codes":[66,104,158],"under":[67],"these":[68],"mappings.":[70],"show":[72],"that":[73],"if":[74],"C":[75,89],"a":[77,117,153],"k-additive":[86],"code,":[87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u22a5":[92,110],"its":[94],"dual,":[95],"then":[96],"of":[100,120,155],"p-ary":[103],"\u03c6(C)":[105],"\u03a6(C":[107],")":[111],"formally":[113],"dual.":[114],"This":[115],"partial":[118],"generalization":[119],"[D.":[121],"S.":[122],"Krotov,":[123],"On":[124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2":[128],"k-dual":[129],"binary":[130],"codes,":[131],"IEEE":[132],"Transactions":[133],"Information":[134],"Theory":[135],"53":[136],"(2007),":[137],"1532-1537],":[138],"result":[141],"generalized":[143],"odd":[145],"characteristic":[146],"mixed":[149,161],"alphabet.":[150],"addition,":[152],"construction":[154],"1-perfect":[156],"additive":[157],"in":[159],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2":[172],"...":[173],"k":[178],"alphabet":[179],"given.":[181]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2889940767","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2025-04-21T11:29:17.373508","created_date":"2018-09-27"}