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The upper bound on the nonlinearity of nonsingular Boolean functions is investigated. We also present [Formula: see text]-variable nonsingular Boolean functions with algebraic degree [Formula: see text] and highest possible nonlinearity for odd [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0129054119500151","type":"journal-article","created":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T04:19:39Z","timestamp":1556597979000},"page":"469-487","source":"Crossref","is-referenced-by-count":0,"title":["Nonsingular Polynomials from Feedback Shift Registers"],"prefix":"10.1142","volume":"30","author":[{"given":"Xiaofang","family":"Xu","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, P. R. China"},{"name":"School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, P. R. 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