{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T06:28:29Z","timestamp":1725604109957},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642235672"},{"type":"electronic","value":"9783642235689"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-23568-9_1","type":"book-chapter","created":{"date-parts":[[2011,8,31]],"date-time":"2011-08-31T00:37:54Z","timestamp":1314751074000},"page":"1-9","source":"Crossref","is-referenced-by-count":3,"title":["A Recurrent Method for Constructing Irreducible Polynomials over Finite Fields"],"prefix":"10.1007","author":[{"given":"Sergey","family":"Abrahamyan","sequence":"first","affiliation":[]},{"given":"Melsik","family":"Kyureghyan","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"1_CR1","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1017\/S0305004100045023","volume":"66","author":"S. Cohen","year":"1969","unstructured":"Cohen, S.: On irreducible polynomials of certain types in finite fields. Proc. Cambridge Philos. Soc.\u00a066, 335\u2013344 (1969)","journal-title":"Proc. Cambridge Philos. Soc."},{"key":"1_CR2","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/S1071-5797(02)00005-9","volume":"9","author":"M. Kyuregyan","year":"2003","unstructured":"Kyuregyan, M.: Recurrent methods for constructing irreducible polynomials over \n                  \n                    \n                  \n                  $\\mathbb{F}_q$\n                 of odd characteristics. Finite Fields Appl. 9, 39\u201358 (2003)","journal-title":"Finite Fields Appl."},{"key":"1_CR3","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/j.ffa.2003.09.002","volume":"10","author":"M. Kyuregyan","year":"2004","unstructured":"Kyuregyan, M.: Iterated constructions of irreducible polynomials over finite fields with linearly independent roots. Finite Fields Appl.\u00a010, 323\u2013431 (2004)","journal-title":"Finite Fields Appl."},{"key":"1_CR4","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.ffa.2005.07.002","volume":"12","author":"M. Kyuregyan","year":"2006","unstructured":"Kyuregyan, M.: Recurrent methods for constructing irreducible polynomials over \n                  \n                    \n                  \n                  $\\mathbb{F}_q$\n                 of odd characteristics II. Finite Fields Appl.\u00a012, 357\u2013378 (2006)","journal-title":"Finite Fields Appl."},{"key":"1_CR5","doi-asserted-by":"crossref","unstructured":"Kyuregyan, M., Kyuregyan, G.: Irreducible Compositions of Polynomials over Finite Fields, Design, Codes and Cryptography (2010), doi:10.1007\/s10623-010-9478-5","DOI":"10.1007\/s10623-010-9478-5"},{"key":"1_CR6","volume-title":"Finite Fields","author":"R. Lidl","year":"1987","unstructured":"Lidl, R., Niederreiter, H.: Finite Fields. Cambridge University Press, Cambridge (1987)"},{"key":"1_CR7","volume-title":"The Theory of Error-Correcting Codes","author":"F.J. MacWilliams","year":"1977","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, New York (1977)"},{"key":"1_CR8","volume-title":"Applications of Finite Fields","author":"A. Menezes","year":"1993","unstructured":"Menezes, A., Blake, I.F., Gao, X., Mullin, R.C., Vanstone, S.A., Yaghoobian, T.: Applications of Finite Fields. Kluwer Academic Publishers, Boston (1993)"},{"key":"1_CR9","volume-title":"Handbook of Applied Cryptography","author":"A. Menezes","year":"1997","unstructured":"Menezes, A., Van Oorschoot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)"},{"key":"1_CR10","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/BF01810846","volume":"1","author":"H. Meyn","year":"1990","unstructured":"Meyn, H.: On the construction of irreducible self-rec iprocal polynomials over finite fields. Appl. Algebrain Eng. Commun. Comput.\u00a01, 43\u201353 (1990)","journal-title":"Appl. Algebrain Eng. Commun. Comput."},{"key":"#cr-split#-1_CR11.1","unstructured":"Moisio, M.: Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and norm, arXiv:0706.2112v5 [math.NT] (November 21, 2007);"},{"key":"#cr-split#-1_CR11.2","unstructured":"Comment: 21 pages; revised version with somewhat more clearer proofs; to appear in Acta Arithmetica"},{"key":"1_CR12","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/0022-314X(71)90038-2","volume":"3","author":"R. Ree","year":"1971","unstructured":"Ree, R.: Proof of a conjecture of S. Chowla. J. Number Theory\u00a03, 210\u2013212 (1971)","journal-title":"Chowla. J. Number Theory"},{"key":"1_CR13","first-page":"334","volume":"29","author":"R. Varshamov","year":"1984","unstructured":"Varshamov, R.: A general method of synthesizing irreducible polynomials over Galois fields. Soviet Math. Dokl.\u00a029, 334\u2013336 (1984)","journal-title":"Soviet Math. Dokl."},{"key":"1_CR14","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1090\/S0025-5718-97-00835-1","volume":"219","author":"D. Wan","year":"1997","unstructured":"Wan, D.: Generators and irreducible polynomials over finite fields. Math. Comp.\u00a0219, 1195\u20131212 (1997)","journal-title":"Math. Comp."},{"key":"1_CR15","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.ffa.2005.04.006","volume":"12","author":"J.L. Yucas","year":"2006","unstructured":"Yucas, J.L.: Irreducible polynomials over finite fields with prescribed trace\/prescribed constant term. Finite Fields and Their Applications\u00a012, 211\u2013221 (2006)","journal-title":"Finite Fields and Their Applications"},{"issue":"3","key":"1_CR16","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1016\/j.ffa.2006.03.002","volume":"13","author":"J.L. Yucas","year":"2007","unstructured":"Yucas, J.L.: Generalized reciprocals, factors of Dickson polynomials and generalized cyclotomic polynomials over finite fields. Finite Fields and Their Applications\u00a013(3), 492\u2013515 (2007)","journal-title":"Finite Fields and Their Applications"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-23568-9_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T16:29:37Z","timestamp":1554136177000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-23568-9_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642235672","9783642235689"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-23568-9_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}