{"id":"https://openalex.org/W2606030710","doi":"https://doi.org/10.1109/tit.2017.2695219","title":"Splitter Sets and $k$ -Radius Sequences","display_name":"Splitter Sets and $k$ -Radius Sequences","publication_year":2017,"publication_date":"2017-04-18","ids":{"openalex":"https://openalex.org/W2606030710","doi":"https://doi.org/10.1109/tit.2017.2695219","mag":"2606030710"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2695219","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2695219","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":["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/A5100375868","display_name":"Tao Zhang","orcid":"https://orcid.org/0000-0002-9914-0382"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, Hangzhou, China","School of Mathematical Sciences Zhejiang University Hangzhou China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"School of Mathematical Sciences Zhejiang University Hangzhou China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046105120","display_name":"Xiande Zhang","orcid":"https://orcid.org/0000-0003-4234-3610"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiande Zhang","raw_affiliation_strings":["School of Mathematical Sciences, University of Science and Technology of China, Hefei, China","School of Mathematical Sciences, University of Science and Technology of China, Hefei, China;"],"raw_orcid":"https://orcid.org/0000-0003-4234-3610","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Science and Technology of China, Hefei, China;","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029449317","display_name":"Gennian Ge","orcid":"https://orcid.org/0000-0002-1535-0754"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gennian Ge","raw_affiliation_strings":["School of Mathematics and Information Science, Guangzhou University, Guangzhou, China","School of Mathematics and Information Science Guangzhou University  Guangzhou China"],"raw_orcid":"https://orcid.org/0000-0002-1535-0754","affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Guangzhou University, Guangzhou, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Mathematics and Information Science Guangzhou University  Guangzhou China","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6896,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.84936237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"63","issue":"12","first_page":"7633","last_page":"7645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/conjecture","display_name":"Conjecture","score":0.7602839469909668},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.7072197198867798},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6417221426963806},{"id":"https://openalex.org/keywords/splitter","display_name":"Splitter","score":0.612752377986908},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.43890637159347534},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4041668176651001},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4031516909599304},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.234537273645401},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14332008361816406}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7602839469909668},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.7072197198867798},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6417221426963806},{"id":"https://openalex.org/C2777403171","wikidata":"https://www.wikidata.org/wiki/Q7578732","display_name":"Splitter","level":2,"score":0.612752377986908},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.43890637159347534},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4041668176651001},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4031516909599304},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.234537273645401},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14332008361816406},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2017.2695219","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2695219","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1391304095","display_name":"\u4fe1\u606f\u53ef\u9760\u5b58\u50a8\u4e0e\u4f20\u8f93\u53ca\u5b89\u5168\u4fdd\u62a4\u4e2d\u51e0\u7c7b\u7f16\u7801\u7814\u7a76","funder_award_id":"61571310","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2946405534","display_name":null,"funder_award_id":"11301503","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8454121759","display_name":null,"funder_award_id":"11431003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W596647513","https://openalex.org/W1507527194","https://openalex.org/W1554544277","https://openalex.org/W1578772172","https://openalex.org/W1665464119","https://openalex.org/W1971490557","https://openalex.org/W1972783627","https://openalex.org/W1986166912","https://openalex.org/W1988374660","https://openalex.org/W1993216293","https://openalex.org/W2030243808","https://openalex.org/W2032605678","https://openalex.org/W2034099424","https://openalex.org/W2045168812","https://openalex.org/W2047433509","https://openalex.org/W2067495494","https://openalex.org/W2073065601","https://openalex.org/W2087496583","https://openalex.org/W2088119478","https://openalex.org/W2094778363","https://openalex.org/W2096408325","https://openalex.org/W2101520845","https://openalex.org/W2102628331","https://openalex.org/W2116091101","https://openalex.org/W2120262149","https://openalex.org/W2132040768","https://openalex.org/W2134825415","https://openalex.org/W2150237827","https://openalex.org/W2295771124","https://openalex.org/W2474914300","https://openalex.org/W2524108521","https://openalex.org/W2550510000","https://openalex.org/W2599650818","https://openalex.org/W2963053721","https://openalex.org/W4230659860","https://openalex.org/W4234803039","https://openalex.org/W6780398462"],"related_works":["https://openalex.org/W2125532919","https://openalex.org/W2119857390","https://openalex.org/W2329750440","https://openalex.org/W3135345069","https://openalex.org/W3113134525","https://openalex.org/W2542987661","https://openalex.org/W1968853115","https://openalex.org/W2031005964","https://openalex.org/W4250898657","https://openalex.org/W2376200199"],"abstract_inverted_index":{"Splitter":[0],"sets":[1,40,58],"are":[2],"closely":[3],"related":[4],"to":[5,56],"lattice":[6],"tilings,":[7],"and":[8,14,59,168],"have":[9],"applications":[10],"in":[11,28],"flash":[12],"memories":[13],"conflict-avoiding":[15,89],"codes.":[16,90],"The":[17],"study":[18],"of":[19,38,44,67,97,104,110,127,153],"k-radius":[20,42,60,99,156],"sequences":[21,43,100],"was":[22],"motivated":[23],"by":[24,106,165],"some":[25,64,74,84],"problems":[26],"occurring":[27],"large":[29],"data":[30],"transfer.":[31],"It":[32],"is":[33],"observed":[34],"that":[35,117,130],"the":[36,108,150],"existence":[37,109],"splitter":[39,57,69],"yields":[41],"short":[45,98],"length.":[46],"In":[47,113],"this":[48],"paper,":[49],"we":[50,82,92,115],"obtain":[51,83],"several":[52,94],"new":[53,65,85],"results":[54,76,86],"contributing":[55],"sequences.":[61,112],"We":[62],"give":[63],"constructions":[66,96],"perfect":[68],"sets,":[70],"as":[71,73],"well":[72],"nonexistence":[75],"on":[77,87],"them.":[78],"As":[79],"a":[80,162],"byproduct,":[81],"optimal":[88],"Furthermore,":[91],"provide":[93],"explicit":[95],"for":[101,118],"certain":[102],"values":[103,126],"n,":[105],"establishing":[107],"k-additive":[111],"particular,":[114],"show":[116],"any":[119],"fixed":[120],"k,":[121],"there":[122],"exist":[123],"infinitely":[124],"many":[125],"n":[128],"such":[129],"f":[131,144],"<sub":[132,145],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[133,139,146],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sub>":[134,147],"(n)":[135,148],"=":[136],"2k/n":[137],"<sup":[138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[140],"+":[141],"O(n),":[142],"where":[143],"denotes":[149],"shortest":[151],"length":[152],"an":[154],"n-ary":[155],"sequence.":[157],"This":[158],"result":[159],"partially":[160],"affirms":[161],"conjecture":[163],"posed":[164],"Bondy,":[166],"Lonc,":[167],"Rza\u0327\u017cewski.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
