{"id":"https://openalex.org/W3110106201","doi":"https://doi.org/10.1142/s012905412050032x","title":"New Constructions of Codebooks Nearly Meeting the Welch Bound","display_name":"New Constructions of Codebooks Nearly Meeting the Welch Bound","publication_year":2020,"publication_date":"2020-11-01","ids":{"openalex":"https://openalex.org/W3110106201","doi":"https://doi.org/10.1142/s012905412050032x","mag":"3110106201"},"language":"en","primary_location":{"id":"doi:10.1142/s012905412050032x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905412050032x","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5028238705","display_name":"Zexia Shi","orcid":"https://orcid.org/0000-0002-9468-0654"},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zexia Shi","raw_affiliation_strings":["School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-9468-0654","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, P. R. China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101926392","display_name":"Lei Sun","orcid":"https://orcid.org/0000-0003-1992-5225"},"institutions":[{"id":"https://openalex.org/I113992204","display_name":"Hebei University of Economics and Business","ror":"https://ror.org/05j1kc284","country_code":"CN","type":"education","lineage":["https://openalex.org/I113992204"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Sun","raw_affiliation_strings":["School of Information Technology, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Technology, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. China","institution_ids":["https://openalex.org/I113992204"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063946169","display_name":"Fang\u2010Wei Fu","orcid":"https://orcid.org/0000-0002-9696-8977"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fang-Wei Fu","raw_affiliation_strings":["Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028238705"],"corresponding_institution_ids":["https://openalex.org/I94611258"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1651644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"07","first_page":"875","last_page":"889"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9973000288009644,"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":0.9836999773979187,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6284704208374023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.613294243812561},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6075057983398438},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5995359420776367},{"id":"https://openalex.org/keywords/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.5767240524291992},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5643721222877502},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.546829342842102},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5448184013366699},{"id":"https://openalex.org/keywords/codebook","display_name":"Codebook","score":0.5104164481163025},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45144766569137573},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4371323585510254},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3313159942626953},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1557113230228424},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09826546907424927}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6284704208374023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.613294243812561},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6075057983398438},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5995359420776367},{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.5767240524291992},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5643721222877502},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.546829342842102},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5448184013366699},{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.5104164481163025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45144766569137573},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4371323585510254},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3313159942626953},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1557113230228424},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09826546907424927},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"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":1,"locations":[{"id":"doi:10.1142/s012905412050032x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s012905412050032x","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[{"id":"https://openalex.org/G2301527561","display_name":null,"funder_award_id":"61571243","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8149715920","display_name":null,"funder_award_id":"F2019207112","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"},{"id":"https://openalex.org/G8633788293","display_name":null,"funder_award_id":"61902107","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/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1542496577","https://openalex.org/W1971917606","https://openalex.org/W1971946972","https://openalex.org/W1973378877","https://openalex.org/W2020089954","https://openalex.org/W2035469609","https://openalex.org/W2045264273","https://openalex.org/W2054194065","https://openalex.org/W2072704718","https://openalex.org/W2083860674","https://openalex.org/W2085618526","https://openalex.org/W2086869478","https://openalex.org/W2094366212","https://openalex.org/W2109672127","https://openalex.org/W2110673833","https://openalex.org/W2118515741","https://openalex.org/W2119667497","https://openalex.org/W2121743251","https://openalex.org/W2125202015","https://openalex.org/W2138548210","https://openalex.org/W2169607109","https://openalex.org/W2465189940","https://openalex.org/W2600271650","https://openalex.org/W2605907766","https://openalex.org/W2768518515","https://openalex.org/W2800824112","https://openalex.org/W2963256081","https://openalex.org/W2964262548","https://openalex.org/W4205892183","https://openalex.org/W4243205024","https://openalex.org/W4292170079"],"related_works":["https://openalex.org/W2293149949","https://openalex.org/W2026099691","https://openalex.org/W4284672201","https://openalex.org/W2377486419","https://openalex.org/W2943202426","https://openalex.org/W2950156284","https://openalex.org/W2736714427","https://openalex.org/W2163679795","https://openalex.org/W2137816434","https://openalex.org/W2777710427"],"abstract_inverted_index":{"Optimal":[0],"codebooks":[1,45,60,101,108],"meeting":[2,47,103],"the":[3,48,104],"Welch":[4,49,105],"bound":[5],"with":[6,88],"equality":[7],"are":[8],"desirable":[9],"in":[10],"many":[11],"areas,":[12],"such":[13,33],"as":[14],"direct":[15],"spread":[16],"code":[17],"division":[18],"multiple":[19],"access":[20],"communications,":[21],"compressed":[22],"sensing":[23],"and":[24,80,112],"so":[25],"on.":[26],"However,":[27],"it":[28],"is":[29,77,84,136],"difficult":[30],"to":[31,43,69,132],"construct":[32,44],"optimal":[34],"codebooks.":[35],"There":[36],"have":[37,109,114],"been":[38],"a":[39,56,78,85,115,121],"number":[40],"of":[41,59,100,123],"attempts":[42],"nearly":[46,102],"bound.":[50,106],"In":[51,119],"this":[52,93],"paper,":[53],"we":[54,95],"introduce":[55],"generic":[57],"construction":[58],"using":[61],"generalized":[62,125],"bent":[63,126],"functions":[64,127],"from":[65,128],"[Formula:":[66,70,74,81,89,129,133],"see":[67,71,75,82,90,130,134],"text]":[68,76,83,131,135],"text],":[72],"where":[73],"prime":[79],"positive":[86],"integer":[87],"text].":[91],"With":[92],"construction,":[94],"obtain":[96],"two":[97],"new":[98,110],"families":[99],"These":[107],"parameters":[111],"could":[113],"small":[116],"alphabet":[117],"size.":[118],"particular,":[120],"class":[122],"regular":[124],"presented.":[137]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}