{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T13:53:39Z","timestamp":1774187619662,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,11,30]],"date-time":"2016-11-30T00:00:00Z","timestamp":1480464000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["11271005"],"award-info":[{"award-number":["11271005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2017,11]]},"DOI":"10.1007\/s10623-016-0312-6","type":"journal-article","created":{"date-parts":[[2016,11,30]],"date-time":"2016-11-30T09:48:18Z","timestamp":1480499298000},"page":"319-341","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Nonlinear functions and difference sets on group actions"],"prefix":"10.1007","volume":"85","author":[{"given":"Yun","family":"Fan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8543-3128","authenticated-orcid":false,"given":"Bangteng","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,11,30]]},"reference":[{"key":"312_CR1","volume-title":"Groups and Representations, GTM 162","author":"JL Alperin","year":"1997","unstructured":"Alperin J.L., Bell R.B.: Groups and Representations, GTM 162. Springer, New York (1997)."},{"issue":"7","key":"312_CR2","doi-asserted-by":"crossref","first-page":"2934","DOI":"10.1109\/18.959271","volume":"47","author":"KT Arasu","year":"2001","unstructured":"Arasu K.T., Ding C., Helleseth T., Kumar P.V., Martinsen H.: Almost difference sets and their sequences with optimal autocorrelations. IEEE Trans. Inf. Theory 47(7), 2934\u20132943 (2001).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"312_CR3","volume-title":"Design Theory","author":"T Beth","year":"1999","unstructured":"Beth T., Jungnickel D., Lenz H.: Design Theory, 2nd edn. Cambridge University Press, Cambridge (1999).","edition":"2"},{"key":"312_CR4","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.jco.2003.08.008","volume":"20","author":"C Carlet","year":"2004","unstructured":"Carlet C., Ding C.: Highly nonlinear mappings. J. Complex. 20, 205\u2013244 (2004).","journal-title":"J. Complex."},{"key":"312_CR5","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/18.42198","volume":"35","author":"H Chung","year":"1989","unstructured":"Chung H., Kumar P.V.: A new general construction of generalized bent functions. IEEE Trans. Inf. Theory 35, 206\u2013209 (1989).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"312_CR6","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10623-007-9137-7","volume":"46","author":"JA Davis","year":"2008","unstructured":"Davis J.A., Poinsot L.: \n                        $$G$$\n                        \n                            \n                                            \n                                G\n                            \n                        \n                    -perfect nonlinear functions. Des. Codes Cryptogr. 46, 83\u201396 (2008).","journal-title":"Des. Codes Cryptogr."},{"key":"312_CR7","unstructured":"Dillon J.F.: Elementary Hadamard difference sets. Ph.D. thesis, University of Maryland, College Park (1974)."},{"key":"312_CR8","doi-asserted-by":"publisher","unstructured":"Fan Y., Xu B.: Fourier transforms and bent functions on faithful actions of finite abelian groups. Des. Codes Cryptogr. (2016). doi:\n                        10.1007\/s10623-016-0177-8\n                        \n                    .","DOI":"10.1007\/s10623-016-0177-8"},{"key":"312_CR9","doi-asserted-by":"crossref","DOI":"10.1515\/9783110809237","volume-title":"Character Theory of Finite Groups","author":"B Huppert","year":"1998","unstructured":"Huppert B.: Character Theory of Finite Groups. Walter de Gruyter, Berlin (1998)."},{"key":"312_CR10","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0097-3165(85)90049-4","volume":"40","author":"PV Kumar","year":"1985","unstructured":"Kumar P.V., Scholtz R.A., Welch L.R.: Generalized bent functions and their properties. J. Comb. Theory Ser. A 40, 90\u2013107 (1985).","journal-title":"J. Comb. Theory Ser. A"},{"key":"312_CR11","doi-asserted-by":"crossref","unstructured":"Lai X., Massey J.L.: A proposal for a new block encryption standard. In: Advances in Cryptology-Eurocrypt\u201990. Lecture Notes in Computer Science, vol. 473, pp. 389\u2013404. Springer, New York (1991).","DOI":"10.1007\/3-540-46877-3_35"},{"key":"312_CR12","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1515\/dma.1997.7.6.547","volume":"7","author":"OA Logachev","year":"1997","unstructured":"Logachev O.A., Salnikov A.A., Yashchenko V.V.: Bent functions over a finite abelian group. Discret. Math. Appl. 7, 547\u2013564 (1997).","journal-title":"Discret. Math. Appl."},{"key":"312_CR13","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1080\/09720529.2006.10698084","volume":"9","author":"L Poinsot","year":"2006","unstructured":"Poinsot L.: Bent functions on a finite nonabelian group. J. Discret. Math. Sci. Cryptogr. 9, 349\u2013364 (2006).","journal-title":"J. Discret. Math. Sci. Cryptogr."},{"key":"312_CR14","doi-asserted-by":"crossref","first-page":"1848","DOI":"10.1016\/j.dam.2009.02.001","volume":"157","author":"L Poinsot","year":"2009","unstructured":"Poinsot L.: A new characterization of group action-based perfect nonlinearity. Discret. Appl. Math. 157, 1848\u20131857 (2009).","journal-title":"Discret. Appl. Math."},{"key":"312_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12095-011-0058-y","volume":"4","author":"L Poinsot","year":"2012","unstructured":"Poinsot L.: Non Abelian bent functions. Cryptogr. Commun. 4, 1\u201323 (2012).","journal-title":"Cryptogr. Commun."},{"key":"312_CR16","first-page":"1","volume":"12","author":"L Poinsot","year":"2005","unstructured":"Poinsot L., Harari S.: Group actions based perfect nonlinearity. GESTS Int. Trans. Comput. Sci. Eng. 12, 1\u201314 (2005).","journal-title":"GESTS Int. Trans. Comput. Sci. Eng."},{"key":"312_CR17","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1142\/S0129054111008751","volume":"22","author":"L Poinsot","year":"2011","unstructured":"Poinsot L., Pott A.: Non-boolean almost perfect nonlinear functions on non-abelian groups. Int. J. Found. Comput. Sci. 22, 1351\u20131367 (2011).","journal-title":"Int. J. Found. Comput. Sci."},{"key":"312_CR18","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S0166-218X(03)00293-2","volume":"138","author":"A Pott","year":"2004","unstructured":"Pott A.: Nonlinear functions in abelian groups and relative diference sets. Optimal discrete structures and algorithms, ODSA 2000. Discret. Appl. Math. 138, 177\u2013193 (2004).","journal-title":"Discret. Appl. Math."},{"key":"312_CR19","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/0097-3165(76)90024-8","volume":"20","author":"OS Rothaus","year":"1976","unstructured":"Rothaus O.S.: On bent functions. J. Comb. Theory Ser. A 20, 300\u2013305 (1976).","journal-title":"J. Comb. Theory Ser. A"},{"key":"312_CR20","volume-title":"Representations of Finite Groups, GTM","author":"J-P Serre","year":"1984","unstructured":"Serre J.-P.: Representations of Finite Groups, GTM. Springer, New York (1984)."},{"key":"312_CR21","doi-asserted-by":"crossref","unstructured":"Shorin V.V., Jelezniakov V.V., Gabidulin E.M.: Linear and differential cryptanalysis of Russian GOST. In: Augot D., Carlet C. (eds.) Workshop on Coding and Cryptography, pp. 467\u2013476 (2001).","DOI":"10.1016\/S1571-0653(04)00206-9"},{"key":"312_CR22","doi-asserted-by":"crossref","first-page":"99","DOI":"10.4213\/dm234","volume":"14","author":"VI Solodovnikov","year":"2002","unstructured":"Solodovnikov V.I.: Bent functions from a finite abelian group to a finite abelian group. Diskret. Mat. 14, 99\u2013113 (2002).","journal-title":"Diskret. Mat."},{"key":"312_CR23","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1134\/S1990478911010133","volume":"5","author":"N Tokareva","year":"2011","unstructured":"Tokareva N.: Generalizations of bent functions: a survey of publications. J. Appl. Ind. Math. 5, 110\u2013129 (2011).","journal-title":"J. Appl. Ind. Math."},{"key":"312_CR24","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.laa.2014.03.033","volume":"452","author":"B Xu","year":"2014","unstructured":"Xu B.: Multidimensional Fourier transforms and nonlinear functions on finite groups. Linear Algebra Appl. 452, 89\u2013105 (2014).","journal-title":"Linear Algebra Appl."},{"key":"312_CR25","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s10623-014-9968-y","volume":"76","author":"B Xu","year":"2015","unstructured":"Xu B.: Bentness and nonlinearity of functions on finite groups. Des. Codes Cryptogr. 76, 409\u2013430 (2015).","journal-title":"Des. Codes Cryptogr."},{"key":"312_CR26","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1016\/j.jpaa.2015.08.007","volume":"220","author":"B Xu","year":"2016","unstructured":"Xu B.: Dual bent functions on finite groups and \n                        $$C$$\n                        \n                            \n                                            \n                                C\n                            \n                        \n                    -algebras. J. Pure Appl. Algebra 220, 1055\u20131073 (2016).","journal-title":"J. Pure Appl. Algebra"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-016-0312-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0312-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0312-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,8,30]],"date-time":"2017-08-30T06:39:15Z","timestamp":1504075155000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-016-0312-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,30]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["312"],"URL":"https:\/\/doi.org\/10.1007\/s10623-016-0312-6","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,30]]}}}