{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T20:11:09Z","timestamp":1769976669615,"version":"3.49.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2014,7,2]],"date-time":"2014-07-02T00:00:00Z","timestamp":1404259200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2014,11]]},"DOI":"10.1007\/s00200-014-0230-7","type":"journal-article","created":{"date-parts":[[2014,7,2]],"date-time":"2014-07-02T08:01:46Z","timestamp":1404288106000},"page":"311-337","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["An extension of the (strong) primitive normal basis theorem"],"prefix":"10.1007","volume":"25","author":[{"given":"Giorgos","family":"Kapetanakis","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,7,2]]},"reference":[{"issue":"3","key":"230_CR1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1090\/S0002-9947-1952-0051869-9","volume":"73","author":"L Carlitz","year":"1952","unstructured":"Carlitz, L.: Primitive roots in finite fields. Trans. Am. Math. Soc. 73(3), 373\u2013382 (1952)","journal-title":"Trans. Am. Math. Soc."},{"issue":"4","key":"230_CR2","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1073\/pnas.38.4.314","volume":"38","author":"L Carlitz","year":"1952","unstructured":"Carlitz, L.: Some problems involving primitive roots in a finite field. Proc. Natl. Acad. Sci. USA 38(4), 314\u2013318 (1952)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"issue":"9","key":"230_CR3","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1090\/S0002-9939-00-05441-1","volume":"128","author":"FN Castro","year":"2000","unstructured":"Castro, F.N., Moreno, C.J.: Mixed exponential sums over finite fields. Proc. Am. Math. Soc. 128(9), 2529\u20132537 (2000)","journal-title":"Proc. Am. Math. Soc."},{"issue":"2","key":"230_CR4","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.jnt.2005.04.001","volume":"116","author":"T Cochrane","year":"2006","unstructured":"Cochrane, T., Pinner, C.: Using Stepanov\u2019s method for exponential sums involving rational functions. J. Number Theory 116(2), 270\u2013292 (2006)","journal-title":"J. Number Theory"},{"issue":"2\u20133","key":"230_CR5","doi-asserted-by":"crossref","first-page":"293","DOI":"10.5486\/PMD.2000.2222","volume":"56","author":"SD Cohen","year":"2000","unstructured":"Cohen, S.D.: Gauss sums and a sieve for generators of Galois fields. Publ. Math. Debrecen 56(2\u20133), 293\u2013312 (2000)","journal-title":"Publ. Math. Debrecen"},{"issue":"3","key":"230_CR6","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.ffa.2005.05.002","volume":"11","author":"SD Cohen","year":"2005","unstructured":"Cohen, S.D.: Explicit theorems on generator polynomials. Finite Fields Appl. 11(3), 337\u2013357 (2005)","journal-title":"Finite Fields Appl."},{"issue":"5","key":"230_CR7","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/s002000050112","volume":"9","author":"SD Cohen","year":"1999","unstructured":"Cohen, S.D., Hachenberger, D.: Primitive normal bases with prescribed trace. Appl. Algebra Eng. Commun. Comput. 9(5), 383\u2013403 (1999)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"1","key":"230_CR8","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1112\/S0024610702003782","volume":"67","author":"SD Cohen","year":"2003","unstructured":"Cohen, S.D., Huczynska, S.: The primitive normal basis theorem\u2014without a computer. J. Lond. Math. Soc. 67(1), 41\u201356 (2003)","journal-title":"J. Lond. Math. Soc."},{"issue":"4","key":"230_CR9","doi-asserted-by":"crossref","first-page":"299","DOI":"10.4064\/aa143-4-1","volume":"143","author":"SD Cohen","year":"2010","unstructured":"Cohen, S.D., Huczynska, S.: The strong primitive normal basis theorem. Acta Arith. 143(4), 299\u2013332 (2010)","journal-title":"Acta Arith."},{"issue":"1","key":"230_CR10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1112\/jlms\/s1-43.1.21","volume":"43","author":"H Davenport","year":"1968","unstructured":"Davenport, H.: Bases for finite fields. J. Lond. Math. Soc. 43(1), 21\u201339 (1968)","journal-title":"J. Lond. Math. Soc."},{"issue":"6","key":"230_CR11","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644\u2013654 (1976)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"230_CR12","unstructured":"Gao, S.: Normal basis over finite fields. Ph.D. thesis, University of Waterloo (1993)"},{"issue":"8","key":"230_CR13","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1016\/j.jpaa.2010.10.015","volume":"215","author":"T Garefalakis","year":"2010","unstructured":"Garefalakis, T.: On the action of $${\\rm GL}_2(\\mathbb{F}_q)$$ GL 2 ( F q ) on irreducible poynomials over $$\\mathbb{F}_q$$ F q . J. Pure Appl. Algebra 215(8), 1835\u20131843 (2010)","journal-title":"J. Pure Appl. Algebra"},{"issue":"1","key":"230_CR14","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0097-3165(84)90015-3","volume":"37","author":"SW Golomb","year":"1984","unstructured":"Golomb, S.W.: Algebraic constructions of Costas arrays. J. Combin. Theory Ser. A 37(1), 13\u201321 (1984)","journal-title":"J. Combin. Theory Ser. A"},{"key":"230_CR15","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1515\/crll.1888.103.230","volume":"103","author":"K Hensel","year":"1888","unstructured":"Hensel, K.: Ueber die darstellung der zahlen eines gattungsbereiches f\u00fcr einen beliebigen primdivisor. J. Reine Angew. Math. 103, 230\u2013237 (1888)","journal-title":"J. Reine Angew. Math."},{"issue":"1","key":"230_CR16","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.jnt.2010.05.011","volume":"131","author":"C Hsu","year":"2011","unstructured":"Hsu, C., Nan, T.: A generalization of the primitive normal basis theorem. J. Number Theory 131(1), 146\u2013157 (2011)","journal-title":"J. Number Theory"},{"key":"230_CR17","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1515\/9783110283600.65","volume-title":"Finite Fields and Their Applications: Character Sums and Polynomials","author":"S Huczynska","year":"2013","unstructured":"Huczynska, S.: Existence results for finite field polynomials with specified properties. In: Charpin, P., Pott, A., Winterhof, A. (eds.) Finite Fields and Their Applications: Character Sums and Polynomials, pp. 65\u201387. De Gruyter, Berlin (2013)"},{"key":"230_CR18","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.ffa.2013.07.004","volume":"24","author":"S Huczynska","year":"2013","unstructured":"Huczynska, S., Mullen, G.L., Panario, D., Thomson, D.: Existence and properties of $$k$$ k -normal elements over finite fields. Finite Fields Appl. 24, 170\u2013183 (2013)","journal-title":"Finite Fields Appl."},{"key":"230_CR19","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.ffa.2013.12.002","volume":"26","author":"G Kapetanakis","year":"2014","unstructured":"Kapetanakis, G.: Normal bases and primitive elements over finite fields. Finite Fields Appl. 26, 123\u2013143 (2014)","journal-title":"Finite Fields Appl."},{"issue":"177","key":"230_CR20","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1090\/S0025-5718-1987-0866111-3","volume":"48","author":"HW Lenstra Jr","year":"1987","unstructured":"Lenstra Jr, H.W., Schoof, R.J.: Primitive normal bases for finite fields. Math. Comput. 48(177), 217\u2013231 (1987)","journal-title":"Math. Comput."},{"key":"230_CR21","volume-title":"Finite Fields","author":"R Lidl","year":"1997","unstructured":"Lidl, R., Niederreiter, H.: Finite Fields, 2nd edn. Cambridge University Press, Cambridge (1997)","edition":"2"},{"issue":"3","key":"230_CR22","first-page":"373","volume":"5","author":"GI Perel\u2019muter","year":"1969","unstructured":"Perel\u2019muter, G.I.: Estimate of a sum along an algebraic curve. Mat. Zametki 5(3), 373\u2013380 (1969)","journal-title":"Mat. Zametki"},{"key":"230_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-6046-0","volume-title":"Number Theory in Function Fields, Grad. Texts in Math.","author":"M Rosen","year":"2002","unstructured":"Rosen, M.: Number Theory in Function Fields, Grad. Texts in Math., vol. 210. Springer, New York (2002)"},{"key":"230_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0080437","volume-title":"Equations over Finite Fields, An Elementary Approach","author":"WM Schmidt","year":"1976","unstructured":"Schmidt, W.M.: Equations over Finite Fields, An Elementary Approach. Springer, Berlin (1976)"},{"issue":"1","key":"230_CR25","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ffa.2011.07.005","volume":"18","author":"H Stichtenoth","year":"2012","unstructured":"Stichtenoth, H., Topuzo\u011flu, A.: Factorization of a class of polynomials over finite fields. Finite Fields Appl. 18(1), 108\u2013122 (2012)","journal-title":"Finite Fields Appl."},{"issue":"3","key":"230_CR26","first-page":"657","volume":"49","author":"T Tian","year":"2006","unstructured":"Tian, T., Qi, W.F.: Primitive normal element and its inverse in finite fields. Acta Math. Sinica (Chin. Ser.) 49(3), 657\u2013668 (2006)","journal-title":"Acta Math. Sinica (Chin. Ser.)"},{"issue":"4","key":"230_CR27","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1016\/j.ffa.2012.04.003","volume":"18","author":"P Wang","year":"2012","unstructured":"Wang, P., Cao, X., Feng, R.: On the existence of some specific elements in finite fields of characteristic 2. Finite Fields Appl. 18(4), 800\u2013813 (2012)","journal-title":"Finite Fields Appl."}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-014-0230-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00200-014-0230-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-014-0230-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T22:52:33Z","timestamp":1689375153000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00200-014-0230-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,2]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2014,11]]}},"alternative-id":["230"],"URL":"https:\/\/doi.org\/10.1007\/s00200-014-0230-7","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7,2]]}}}