{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:32:17Z","timestamp":1740133937493,"version":"3.37.3"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"name":"973 Program of China","award":["2013CB834204"],"award-info":[{"award-number":["2013CB834204"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61571243"],"award-info":[{"award-number":["61571243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Colleges and Universities in Hebei Province Science and Technology Research Project","award":["QN2018105"],"award-info":[{"award-number":["QN2018105"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61902107"],"award-info":[{"award-number":["61902107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2019207112"],"award-info":[{"award-number":["F2019207112"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2020,11]]},"abstract":"<jats:p> Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks using generalized bent functions from [Formula: see text] to [Formula: see text], where [Formula: see text] is a prime and [Formula: see text] is a positive integer with [Formula: see text]. With this construction, we obtain two new families of codebooks nearly meeting the Welch bound. These codebooks have new parameters and could have a small alphabet size. In particular, a class of regular generalized bent functions from [Formula: see text] to [Formula: see text] is presented. <\/jats:p>","DOI":"10.1142\/s012905412050032x","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T09:35:55Z","timestamp":1605864955000},"page":"875-889","source":"Crossref","is-referenced-by-count":0,"title":["New Constructions of Codebooks Nearly Meeting the Welch Bound"],"prefix":"10.1142","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9468-0654","authenticated-orcid":false,"given":"Zexia","family":"Shi","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, P. R. China"}]},{"given":"Lei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Information Technology, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. 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