{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:14:10Z","timestamp":1761059650924},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,1,3]],"date-time":"2014-01-03T00:00:00Z","timestamp":1388707200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2015,5]]},"DOI":"10.1007\/s10623-013-9912-6","type":"journal-article","created":{"date-parts":[[2014,1,2]],"date-time":"2014-01-02T13:59:46Z","timestamp":1388671186000},"page":"281-299","source":"Crossref","is-referenced-by-count":17,"title":["Functions which are PN on infinitely many extensions of $$\\mathbb {F}_p,\\,p$$ F p , p odd"],"prefix":"10.1007","volume":"75","author":[{"given":"Elodie","family":"Leducq","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,1,3]]},"reference":[{"key":"9912_CR1","doi-asserted-by":"crossref","unstructured":"Coulter R.S., Matthews R.W.: Planar functions and planes of Lenz-Barlotti class II. Des. Codes Cryptogr. 10(2), 167\u2013184 (1997).","DOI":"10.1023\/A:1008292303803"},{"key":"9912_CR2","doi-asserted-by":"crossref","unstructured":"Dembowski P., Ostrom T.G.: Planes of order $$n$$ n with collineation groups of order $$n^{2}$$ n 2 . Math. Z. 103, 239\u2013258 (1968).","DOI":"10.1007\/BF01111042"},{"key":"9912_CR3","doi-asserted-by":"crossref","unstructured":"Dobbertin H., Mills D., M\u00fcller E.N., Pott A., Willems A.: APN functions in odd characteristic. Discrete Math. 267(13), 95\u2013112 (2003). Combinatorics 2000 (Gaeta).","DOI":"10.1016\/S0012-365X(02)00606-4"},{"key":"9912_CR4","unstructured":"Fulton W.: Algebraic Curves. Advanced Book Classics. Addison-Wesley Publishing Company Advanced Book Program, Redwood City (1989). An introduction to algebraic geometry, Notes written with the collaboration of Richard Weiss, Reprint of 1969 original."},{"key":"9912_CR5","doi-asserted-by":"crossref","unstructured":"Hernando F., McGuire G.: Proof of a conjecture on the sequence of exceptional numbers, classifying cyclic codes and APN functions. J. Algebra 343, 78\u201392 (2011).","DOI":"10.1016\/j.jalgebra.2011.06.019"},{"key":"9912_CR6","doi-asserted-by":"crossref","unstructured":"Hernando F., McGuire G., Monserrat F.: On the classification of exceptional planar functions over $$\\mathbb{F}_p$$ F p . ArXiv e-prints (2013).","DOI":"10.1007\/s10711-013-9926-2"},{"key":"9912_CR7","doi-asserted-by":"crossref","unstructured":"Janwa H., McGuire G.M., Wilson R.M.: Double-error-correcting cyclic codes and absolutely irreducible polynomials over GF(2). J. Algebra 178(2), 665\u2013676 (1995).","DOI":"10.1006\/jabr.1995.1372"},{"key":"9912_CR8","doi-asserted-by":"crossref","unstructured":"Jedlicka D.: APN monomials over GF $$(2^n)$$ ( 2 n ) for infinitely many $$n$$ n . Finite Fields Appl. 13(4), 1006\u20131028 (2007).","DOI":"10.1016\/j.ffa.2007.04.004"},{"key":"9912_CR9","unstructured":"Lidl R., Niederreiter H.: Finite Fields, Volume 20 of Encyclopedia of Mathematics and its Applications, 2nd edn. Cambridge University Press, Cambridge (1997). With a foreword by P. M. Cohn."},{"key":"9912_CR10","unstructured":"Sorensen A.B.: A note on algorithms deciding rationality and absolutely irreducibility based on the number of rational solutions. RISC report series 91-37, Research Institute for Symbolic Computation (RISC), University of Linz, Hagenberg (1991)."},{"key":"9912_CR11","doi-asserted-by":"crossref","unstructured":"Zieve M.: Planar functions and perfect nonlinear monomials over finite fields. ArXiv e-prints (2013).","DOI":"10.1007\/s10623-013-9890-8"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-013-9912-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-013-9912-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-013-9912-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T18:36:13Z","timestamp":1565030173000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-013-9912-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,3]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,5]]}},"alternative-id":["9912"],"URL":"https:\/\/doi.org\/10.1007\/s10623-013-9912-6","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,3]]}}}