{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T03:25:18Z","timestamp":1782185118158,"version":"3.54.5"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,2,23]],"date-time":"2010-02-23T00:00:00Z","timestamp":1266883200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1007\/s00200-010-0120-6","type":"journal-article","created":{"date-parts":[[2010,2,22]],"date-time":"2010-02-22T04:29:43Z","timestamp":1266812983000},"page":"145-150","source":"Crossref","is-referenced-by-count":53,"title":["Two new permutation polynomials with the form $${\\left(x^{2^k}+x+\\delta\\right)^{s}+x}$$ over $${\\mathbb{F}_{2^n}}$$"],"prefix":"10.1007","volume":"21","author":[{"given":"Xiangyong","family":"Zeng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xishun","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2010,2,23]]},"reference":[{"key":"120_CR1","doi-asserted-by":"crossref","unstructured":"Ball, S., Zieve, M.: Symplectic spreads and permutation polynomials. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds.) International Conference on Finite Fields and Applications, Lecture Notes in Computer Science, vol. 2948, pp. 79\u201388. Springer (2004)","DOI":"10.1007\/978-3-540-24633-6_7"},{"key":"120_CR2","doi-asserted-by":"crossref","unstructured":"Blokhuis, A., Coulter, R.S., Henderson, M., OKeefe, C.M.: Permutations amongst the Dembowski-Ostrom polynomials. In: Jungnickel, D., Niederreiter, H. (eds.) Finite Fields and Applications: Proceedings of the Fifth International Conference on Finite Fields and Applications, pp. 37\u201342 (2001)","DOI":"10.1007\/978-3-642-56755-1_4"},{"key":"120_CR3","doi-asserted-by":"crossref","unstructured":"Beth, T., Ding, C.: On almost perfect nonlinear permutations. In: Goos, G., Hartmanis, J. (eds.) Advances in Cryptology-EUROCRYPT\u201993, Lecture Notes in Computer Science, vol. 765, pp. 65\u201376. Springer (1993)","DOI":"10.1007\/3-540-48285-7_7"},{"key":"120_CR4","unstructured":"Cohen, S.D.: Permutation group theory and permutation polynomials. In: Algebras and Combinatorics, Hong Kong (1997), pp. 133\u2013146. Springer, Singapore (1999)"},{"key":"120_CR5","first-page":"171","volume":"28","author":"R.S. Coulter","year":"1999","unstructured":"Coulter R.S.: On the equivalence of a class of Weil sums in characteristic 2. N. Z. J. Math. 28, 171\u2013184 (1999)","journal-title":"N. Z. J. Math."},{"key":"120_CR6","doi-asserted-by":"crossref","unstructured":"Corrada Bravo, C.J., Kumar, P.V.: Permutation polynomials for interleavers in turbo codes. In: Proceedings of the IEEE International Symposium on Information Theory, Yokohama, Japan, p. 318. 29 June\u20134 July (2003)","DOI":"10.1109\/ISIT.2003.1228333"},{"key":"120_CR7","doi-asserted-by":"crossref","unstructured":"Dobbertin, H.: Kasami power functions, permutation polynomials and cyclic difference sets, difference sets, sequences and their correlation properties (Bad Windsheim, 1998), NATO Advanced Science Institute Series C: Mathematical and Physical Science, vol. 542, pp. 133\u2013158. Kluwer Academic Publishers, Dordrecht (1999)","DOI":"10.1007\/978-94-011-4459-9_6"},{"issue":"2","key":"120_CR8","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S1071-5797(02)00028-X","volume":"9","author":"T. Helleseth","year":"2003","unstructured":"Helleseth T., Zinoviev V.: New Kloosterman sums identities over $${\\mathbb{F}_{2^m}}$$ for all m. Finite Fields Appl. 9(2), 187\u2013193 (2003)","journal-title":"Finite Fields Appl."},{"issue":"1","key":"120_CR9","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.ffa.2004.06.005","volume":"11","author":"H.D. Hollmann","year":"2005","unstructured":"Hollmann H.D., Xiang Q.: A class of permutation polynomials of $${\\mathbb{F}_{2^m}}$$ related to Dickson polynomials. Finite Fields Appl. 11(1), 111\u2013122 (2005)","journal-title":"Finite Fields Appl."},{"issue":"3","key":"120_CR10","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/00029890.1988.11971991","volume":"95","author":"R. Lidl","year":"1988","unstructured":"Lidl R., Mullen G.L.: When does a polynomial over a finite field permute the elements of the field?. Am. Math. Mon. 95(3), 243\u2013246 (1988)","journal-title":"Am. Math. Mon."},{"issue":"1","key":"120_CR11","doi-asserted-by":"crossref","first-page":"71","DOI":"10.2307\/2324822","volume":"100","author":"R. Lidl","year":"1993","unstructured":"Lidl R., Mullen G.L.: When does a polynomial over a finite field permute the elements of the field? II. Am. Math. Mon. 100(1), 71\u201374 (1993)","journal-title":"Am. Math. Mon."},{"key":"120_CR12","volume-title":"Finite Fields, Encyclopedia of Mathematics and its Applications, 2nd ed., vol. 20","author":"R. Lidl","year":"1997","unstructured":"Lidl R., Niederreiter H.: Finite Fields, Encyclopedia of Mathematics and its Applications, 2nd ed., vol. 20. Cambridge University Press, Cambridge (1997)"},{"key":"120_CR13","unstructured":"Mullen, G.L.: Permutation polynomials over finite fields. In: Finite Fields, Coding Theory, and Advances in Communications and Computing (Las Vegas, NV, 1991), Lecture Notes in Pure and Applied Mathematics, vol. 141, pp. 131\u2013151. Dekker, New York (1993)"},{"issue":"4","key":"120_CR14","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1016\/j.ffa.2006.05.006","volume":"13","author":"J. Yuan","year":"2007","unstructured":"Yuan J., Ding C.: Four classes of permutation polynomials of $${\\mathbb{F}_{2^m}}$$ . Finite Fields Appl. 13(4), 869\u2013876 (2007)","journal-title":"Finite Fields Appl."},{"key":"120_CR15","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.ffa.2007.05.003","volume":"14","author":"J. Yuan","year":"2008","unstructured":"Yuan J., Ding C., Wang H., Pieprzyk J.: Permutation polynomials of the form (x p \u2212x\u00a0+\u00a0\u03b4) s \u00a0+\u00a0L(x). Finite Fields Appl. 14, 482\u2013493 (2008)","journal-title":"Finite Fields Appl."},{"key":"120_CR16","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s00200-004-0163-7","volume":"15","author":"W. Zhang","year":"2004","unstructured":"Zhang W., Wu C., Li S.: Construction of cryptographically important Boolean permutations. Appl. Algebra Eng. Commun. Comput. 15, 173\u2013177 (2004)","journal-title":"Appl. Algebra Eng. Commun. Comput."}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-010-0120-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00200-010-0120-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-010-0120-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T01:06:18Z","timestamp":1558832778000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00200-010-0120-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,23]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["120"],"URL":"https:\/\/doi.org\/10.1007\/s00200-010-0120-6","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,23]]}}}