{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T03:19:22Z","timestamp":1773112762397,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61502524"],"award-info":[{"award-number":["61502524"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2020,4]]},"abstract":"<jats:p> In this paper, we propose a new necessary condition for feedback functions of de Bruijn sequences and discuss its application in constructing de Bruijn sequences. It is shown that a large number of de Bruijn sequences could be easily constructed by precomputing an [Formula: see text]-stage nonlinear feedback shift register (NFSR) with a special cycle structure\u2014that is, if a state [Formula: see text] is on a cycle generated by this NFSR, then all the states with the same Hamming weight as [Formula: see text] are also on this cycle. Moreover, if there are [Formula: see text] different cycles in the state graph of the precomputed NFSR, then we can construct [Formula: see text] de Bruijn sequences by the different choices of conjugate state pairs, where [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0129054120500094","type":"journal-article","created":{"date-parts":[[2020,5,4]],"date-time":"2020-05-04T08:07:29Z","timestamp":1588579649000},"page":"301-312","source":"Crossref","is-referenced-by-count":3,"title":["Constructing de Bruijn Sequences Based on a New Necessary Condition"],"prefix":"10.1142","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2410-095X","authenticated-orcid":false,"given":"Zhongxiao","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, P. R. China"}]},{"given":"Xiangyu","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, P. R. China"}]},{"given":"Tian","family":"Tian","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, P. R. 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