{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T04:43:43Z","timestamp":1725684223828},"reference-count":23,"publisher":"Institute of Electronics, Information and Communications Engineers (IEICE)","issue":"9","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEICE Trans. Fundamentals"],"published-print":{"date-parts":[[2021,9,1]]},"DOI":"10.1587\/transfun.2021eal2004","type":"journal-article","created":{"date-parts":[[2021,3,7]],"date-time":"2021-03-07T22:06:39Z","timestamp":1615154799000},"page":"1357-1360","source":"Crossref","is-referenced-by-count":1,"title":["The Explicit Dual of Leander's Monomial Bent Function"],"prefix":"10.1587","volume":"E104.A","author":[{"given":"Yanjun","family":"LI","sequence":"first","affiliation":[{"name":"Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics"}]},{"given":"Haibin","family":"KAN","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Fudan-Zhongan Joint Laboratory of Blockchain and Information Security, Shanghai Engineering Research Center of Blockchain, Key Laboratory for Information Science of Electromagnetic Waves (MoE)"}]},{"given":"Jie","family":"PENG","sequence":"additional","affiliation":[{"name":"Mathematics and Science College, Shanghai Normal University"}]},{"given":"Chik How","family":"TAN","sequence":"additional","affiliation":[{"name":"Temasek Laboratories, National University of Singapore"}]},{"given":"Baixiang","family":"LIU","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Fudan-Zhongan Joint Laboratory of Blockchain and Information Security, Shanghai Engineering Research Center of Blockchain, Key Laboratory for Information Science of Electromagnetic Waves (MoE)"}]}],"member":"532","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] A. Canteaut, P. Charpin, and G. Kyureghyan, \u201cA new class of monomial bent functions,\u201d Finite Fields Appl., vol.14, no.1, pp.221-241, 2008. 10.1016\/j.ffa.2007.02.004","DOI":"10.1016\/j.ffa.2007.02.004"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] L. Carlitz, \u201cSome theorems on permutation polynomials,\u201d Bull. Am. Math. Soc., vol.68, no.2, pp.120-122, 1962. 10.1090\/s0002-9904-1962-10750-2","DOI":"10.1090\/S0002-9904-1962-10750-2"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] L. Carlitz and C. Wells, \u201cThe number of solutions of a special system equations in a finite fields,\u201d Acta Arith., vol.12, pp.77-84, 1966. 10.4064\/aa-12-1-77-84","DOI":"10.4064\/aa-12-1-77-84"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] P. Charpin and G. Kyureghyan, \u201cCubic monomial bent functions: a subclass of <i>M<\/i>,\u201d SIAM J. Discrete Math., vol.22, no.2, pp.650-665, 2008. 10.1137\/060677768","DOI":"10.1137\/060677768"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] R.S. Coulter and M. Henderson, \u201cThe compositional inverse of a class of permutation polynomials over a finite field,\u201d Bull. Aust. Math. Soc., vol.65, no.3, pp.521-526, 2002. 10.1017\/s0004972700020578","DOI":"10.1017\/S0004972700020578"},{"key":"6","unstructured":"[6] J. Dillon, Elementary Hadamard Difference Sets, PhD thesis, Univ. of Maryland, 1974."},{"key":"7","doi-asserted-by":"publisher","unstructured":"[7] X. Hou, \u201cA class of permutation binomials over finite fields,\u201d J. Number Theory, vol.133, no.10, pp.3549-3558, 2013. 10.1016\/j.jnt.2013.04.011","DOI":"10.1016\/j.jnt.2013.04.011"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] X. Hou and S.D. Lappano, \u201cDetermination of a type of permutaiton binomials over finite fields,\u201d J. Number Theory, vol.147, pp.14-23, 2015. 10.1016\/j.jnt.2014.06.021","DOI":"10.1016\/j.jnt.2014.06.021"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] S.D. Lappano, \u201cA note regarding permutation binomials over $\\mathbb{F}_{q^2}$,\u201d Finite Fields Appl., vol.34, pp.153-160, 2015. 10.1016\/j.ffa.2015.01.010","DOI":"10.1016\/j.ffa.2015.01.010"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] N.G. Leander, \u201cMonomial bent functions,\u201d IEEE Trans. Inf. Theory, vol.52, no.2, pp.738-743, 2006. 10.1109\/tit.2005.862121","DOI":"10.1109\/TIT.2005.862121"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] K. Li, L. Qu, and X. Chen, \u201cNew classes of permutation binomials and permutation trinomials over finite fields,\u201d Finite Fields Appl., vol.43, pp.69-85, 2017. 10.1016\/j.ffa.2016.09.002","DOI":"10.1016\/j.ffa.2016.09.002"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] K. Li, L. Qu, and Q. Wang, \u201cCompositional inverses of permutation polynomials of the form <i>x<sup>r<\/sup>h<\/i>(<i>x<sup>s<\/sup><\/i>) over finite fields,\u201d Cryptogr. Commun., vol.11, pp.279-298, 2019. 10.1007\/s12095-018-0292-7","DOI":"10.1007\/s12095-018-0292-7"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] Y. Li and M. Wang, \u201cOn EA-equivalence of certain permutations to power mappings,\u201d Des. Codes Cryptogr., vol.58, pp.259-269, 2011. 10.1007\/s10623-010-9406-8","DOI":"10.1007\/s10623-010-9406-8"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] A.M. Masuda and M.E. Zieve, \u201cPermutation binomials over finite fields,\u201d Trans. Am. Math. Soc., vol.361, pp.4169-4180, 2009. 10.1090\/s0002-9947-09-04578-4","DOI":"10.1090\/S0002-9947-09-04578-4"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] R.-L. McFarland, \u201cA family of noncyclic difference sets,\u201d J. Combin. Theory Ser. A, vol.15, no.1, pp.1-10, 1973. 10.1016\/0097-3165(73)90031-9","DOI":"10.1016\/0097-3165(73)90031-9"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[16] S. Mesnager, \u201cSeveral new infinite families of bent functions and their duals,\u201d IEEE Trans. Inf. Theory, vol.60, no.7, pp.4397-4407, 2014. 10.1109\/tit.2014.2320974","DOI":"10.1109\/TIT.2014.2320974"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] J. Peng, L. Zheng, C. Wu, and H. Kan, \u201cPermutation polynomials $x^{2^{k+1}+3}+ax^{2^k+2}+bx$ over $\\mathbb{F}_{2^{2k}}$ and their differential uniformity,\u201d Sci. China Inf. Sci., vol.63, pp.209101:1-209101:3, 2020. 10.1007\/s11432-018-9741-6","DOI":"10.1007\/s11432-018-9741-6"},{"key":"18","doi-asserted-by":"publisher","unstructured":"[18] O. Rothaus, \u201cOn \u2018bent\u2019 functions,\u201d J. Combin. Theory Ser. A, vol.20, no.3, pp.300-305, 1976. 10.1016\/0097-3165(76)90024-8","DOI":"10.1016\/0097-3165(76)90024-8"},{"key":"19","doi-asserted-by":"publisher","unstructured":"[19] Q. Wang, \u201cOn inverse permutation polynomials,\u201d Finite Fields Appl., vol.15, no.2, pp.207-213, 2009. 10.1016\/j.ffa.2008.12.003","DOI":"10.1016\/j.ffa.2008.12.003"},{"key":"20","doi-asserted-by":"crossref","unstructured":"[20] Q. Wang, \u201cCyclotomic mapping permutation polynomials over finite fields,\u201d Sequences, Subsequences, and Consequences, Lecture Notes in Comput. Sci., vol.4893, pp.119-128, Springer, Berlin, 2007. 10.1007\/978-3-540-77404-4_11","DOI":"10.1007\/978-3-540-77404-4_11"},{"key":"21","doi-asserted-by":"publisher","unstructured":"[21] B. Wu, \u201cThe compositional inverse of a class of linearized permutation polynomials over $\\mathbb{F}_{2^n}$, <i>n<\/i> odd,\u201d Finite Fields Appl., vol.29, pp.34-48, 2014. 10.1016\/j.ffa.2014.03.003","DOI":"10.1016\/j.ffa.2014.03.003"},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] L. Zheng, J. Peng, H. Kan, and Y. Li, \u201cSeveral new infinite families of bent functions via second order derivatives,\u201d Cryptogr. Commun., vol.12, pp.1143-1160, 2020. https:\/\/doi.org\/10.1007\/s12095-020-00436-0 10.1007\/s12095-020-00436-0","DOI":"10.1007\/s12095-020-00436-0"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] Y. Zheng, Q. Wang, and W. Wei, \u201cOn inverses of permutation polynomials of small degree over finite fields,\u201d IEEE Trans. Inf. Theory, vol.66, no.2, pp.914-922, 2020. 10.1109\/TIT.2019.2939113","DOI":"10.1109\/TIT.2019.2939113"}],"container-title":["IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E104.A\/9\/E104.A_2021EAL2004\/_pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,4]],"date-time":"2021-09-04T03:26:49Z","timestamp":1630726009000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E104.A\/9\/E104.A_2021EAL2004\/_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,1]]},"references-count":23,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2021]]}},"URL":"https:\/\/doi.org\/10.1587\/transfun.2021eal2004","relation":{},"ISSN":["0916-8508","1745-1337"],"issn-type":[{"value":"0916-8508","type":"print"},{"value":"1745-1337","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,1]]},"article-number":"2021EAL2004"}}