{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:32:11Z","timestamp":1740133931881,"version":"3.37.3"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"name":"National Key Basic Research Program of China","award":["2013CB834204"],"award-info":[{"award-number":["2013CB834204"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61571243"],"award-info":[{"award-number":["61571243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61171082"],"award-info":[{"award-number":["61171082"]}],"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":[[2017,11]]},"abstract":"<jats:p> In this paper, we study the conjecture that [Formula: see text]-variable ([Formula: see text] odd) rotation symmetric Boolean functions with degree [Formula: see text] have no non-zero linear structures. We show that if this class of RSBFs have non-zero linear structures, then the linear structures are invariant linear structures and the homogeneous component of degree [Formula: see text] in the function\u2019s algebraic normal form has only two possibilities. Moreover, it is checked that the conjecture is true for [Formula: see text], and then a more explicit conjecture is proposed. <\/jats:p>","DOI":"10.1142\/s0129054117500265","type":"journal-article","created":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T03:50:52Z","timestamp":1519357852000},"page":"819-833","source":"Crossref","is-referenced-by-count":1,"title":["On the Conjecture About the Linear Structures of Rotation Symmetric Boolean Functions"],"prefix":"10.1142","volume":"28","author":[{"given":"Lei","family":"Sun","sequence":"first","affiliation":[{"name":"Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China"}]},{"given":"Fangwei","family":"Fu","sequence":"additional","affiliation":[{"name":"Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. 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