{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T13:10:20Z","timestamp":1776863420827,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":28,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540579366","type":"print"},{"value":"9783540483922","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1994]]},"DOI":"10.1007\/3-540-57936-2_27","type":"book-chapter","created":{"date-parts":[[2012,2,26]],"date-time":"2012-02-26T13:41:28Z","timestamp":1330263688000},"page":"1-23","source":"Crossref","is-referenced-by-count":14,"title":["Constructive problems for irreducible polynomials over finite fields"],"prefix":"10.1007","author":[{"given":"Ian F.","family":"Blake","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuhong","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Lambert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,6,6]]},"reference":[{"key":"1_CR1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF01386832","volume":"4","author":"I.F. Blake","year":"1993","unstructured":"I.F. Blake, S. Gao and R.C. Mullin, \u201cExplicit factorization of $$x^{2^k } + 1$$ over F p with prime p\u22613 mod 4\u201d, AAECC, 4 (1993), pp. 89\u201394.","journal-title":"AAECC"},{"key":"1_CR2","doi-asserted-by":"crossref","unstructured":"J. Brillhart, D.H. Lehmer, J.L. Selfridge, B. Tuckerman and S.S. Wagstaff, \u201cFactorizations of b n \u00b11, b=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers\u201d, Vol. 22 of Contemporary Mathematics, AMS, 1988, 2nd edition.","DOI":"10.1090\/conm\/022"},{"key":"1_CR3","doi-asserted-by":"crossref","first-page":"603","DOI":"10.2140\/pjm.1970.32.603","volume":"32","author":"L. Carlitz","year":"1970","unstructured":"L. Carlitz, \u201cFactorization of a special polynomial over a finite field\u201d, Pac. J. Math., 32 (1970) pp. 603\u2013614.","journal-title":"Pac. J. Math."},{"key":"1_CR4","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0022-247X(66)90136-3","volume":"15","author":"S. Chowla","year":"1966","unstructured":"S. Chowla, \u201cA note on the construction of finite Galois fields GF(p n )\u201d, J. Math. Anal. Appl., 15 (1966), pp. 53\u201354. in 335\u2013344.","journal-title":"J. Math. Anal. Appl."},{"key":"1_CR5","doi-asserted-by":"crossref","first-page":"255","DOI":"10.4064\/aa-17-3-255-271","volume":"17","author":"S.D. Cohen","year":"1970","unstructured":"S.D. Cohen, \u201cThe distribution of polynomials over finite fields\u201d, Acta Arith., 17 1970, pp. 255\u2013271.","journal-title":"Acta Arith."},{"key":"1_CR6","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/S0019-9958(81)90144-3","volume":"50","author":"H. Fredricksen","year":"1981","unstructured":"H. Fredricksen and R. Wisniewski, \u201cOn trinomials x n +x 2+1 and x 81\u00b13 +x k+1 irreducible over GF(2)\u201d, Information and Control, 50 (1981) pp. 58\u201363.","journal-title":"Information and Control"},{"key":"1_CR7","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF01272074","volume":"2","author":"J. Gathen von zur","year":"1992","unstructured":"J. von zur Gathen and V. Shoup, \u201cComputing Frobenius maps and factoring polynomials\u201d, Computational Complexity, 2 (1992), pp. 187\u2013224.","journal-title":"Computational Complexity"},{"key":"1_CR8","unstructured":"S.W. Golomb, Shift Register Sequences, Holden-Day Inc., 1967."},{"key":"1_CR9","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1090\/S0025-5718-1992-1134730-7","volume":"59","author":"T. Hansen","year":"1992","unstructured":"T. Hansen and G.L. Mullen, \u201cPrimitive polynomials over finite fields\u201d, Math. Comp., 59 (1992) 639\u2013643.","journal-title":"Math. Comp."},{"key":"1_CR10","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1142\/S0129183192000361","volume":"3","author":"J.R. Heringa","year":"1992","unstructured":"J.R. Heringa, H.W.J. Bl\u0150te and A, Compagner, \u201cNew primitive trinomials of Mersenneexponent degrees for random-number generation\u201d, Int'l J. Modern Physics C, 3 (1992) 561\u2013564.","journal-title":"Int'l J. Modern Physics C"},{"key":"1_CR11","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1090\/S0025-5718-1987-0866111-3","volume":"48","author":"H.W. Lenstra","year":"1987","unstructured":"H.W. Lenstra and R.J. Schoof, \u201cPrimitive normal bases for finite fields\u201d, Math. Comp., 48 (1987) pp. 217\u2013231.","journal-title":"Math. Comp."},{"key":"1_CR12","unstructured":"R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, 1987."},{"key":"1_CR13","doi-asserted-by":"crossref","first-page":"175","DOI":"10.2140\/pjm.1981.96.175","volume":"96","author":"R.W. Marsh","year":"1981","unstructured":"R.W. Marsh, W.H. Mills, R.L. Ward, H. Rumsey Jr. and L.R. Welch, \u201cRound trinomials\u201d, Pac. J. Math., 96 (1981) pp. 175\u2013192. self-reciprocal 43\u201353.","journal-title":"Pac. J. Math."},{"key":"1_CR14","first-page":"860","volume":"25","author":"W.H. Mills","year":"1970","unstructured":"W.H. Mills, \u201cThe degrees of the factors of certain polynomials over finite fields\u201d, Proc. Amer. Math. Soc., 25 (1970) pp. 860\u2013863.","journal-title":"Proc. Amer. Math. Soc."},{"key":"1_CR15","doi-asserted-by":"crossref","first-page":"635","DOI":"10.2140\/pjm.1969.28.635","volume":"28","author":"W.H. Mills","year":"1969","unstructured":"W.H. Mills and N. Zierler, \u201cOn a conjecture of Golomb\u201d, Pac. J. Math., 28 (1969) pp. 635\u2013640.","journal-title":"Pac. J. Math."},{"key":"1_CR16","unstructured":"A.J. Menezes, editor, Applications of Finite fields, Kluwer Academic Publishers, 1993."},{"key":"1_CR17","doi-asserted-by":"crossref","unstructured":"A. Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, Proc. Eurocrypt '84, pp. 224\u2013314.","DOI":"10.1007\/3-540-39757-4_20"},{"key":"1_CR18","unstructured":"A. Odlyzko, Asymptotic enumeration methods, manuscript, 1993."},{"key":"1_CR19","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/0022-314X(71)90038-2","volume":"3","author":"R. Ree","year":"1971","unstructured":"R. Ree, \u201cProof of a conjecture of S. Chowla\u201d, J. of Number Theory, 3 (1971), pp. 210\u2013212.","journal-title":"J. of Number Theory"},{"key":"1_CR20","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1090\/S0025-5718-1968-0238813-1","volume":"22","author":"E.R. Rodemich","year":"1968","unstructured":"E.R. Rodemich and H. Rumsey Jr., \u201cPrimitive polynomials of high degree\u201d, Math. Comp., 22 (1968) pp.863\u2013865.","journal-title":"Math. Comp."},{"key":"1_CR21","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1090\/S0025-5718-1992-1106981-9","volume":"58","author":"V. Shoup","year":"1992","unstructured":"V. Shoup, \u201cSearching for primitive roots in finite fields\u201d, Math. Comp., 58 (1992), pp. 369\u2013380.","journal-title":"Math. Comp."},{"key":"1_CR22","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1070\/RM1991v046n01ABEH002725","volume":"46","author":"I.E. Shparlinskii","year":"1991","unstructured":"I.E. Shparlinskii, \u201cOn some problems in the theory of finite fields\u201d, Russian Math. Surveys, 46 (1991), pp. 199\u2013240; or Uspekhi Mat. Nauk, 46 (1991), pp. 165\u2013200.","journal-title":"Russian Math. Surveys"},{"key":"1_CR23","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.2140\/pjm.1962.12.1099","volume":"12","author":"R.G. Swan","year":"1962","unstructured":"R.G. Swan, \u201cFactorization of polynomials over finite fields\u201d. Pac. J. Math., 12 (1962) 1099\u20131106.","journal-title":"Pac. J. Math."},{"key":"1_CR24","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1016\/S0019-9958(68)90973-X","volume":"13","author":"N. Zierler","year":"1968","unstructured":"N. Zierler and J. Brillhart, \u201cOn primitive trinomials (Mod 2)\u201d, Information and Control, 13 (1968) pp. 541\u2013554.","journal-title":"Information and Control"},{"key":"1_CR25","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1016\/S0019-9958(69)90356-8","volume":"14","author":"N. Zierler","year":"1969","unstructured":"N. Zierler and J. Brillhart, \u201cOn primitive trinomials(Mod 2), II\u201d, Information and Control, 14 (1969) pp. 566\u2013569.","journal-title":"Information and Control"},{"key":"1_CR26","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1016\/S0019-9958(70)90264-0","volume":"16","author":"N. Zierler","year":"1970","unstructured":"N. Zierler, \u201cOn x n+x+1 over GF(2)\u201d, Information and Control, 16 (1970) pp. 502\u2013505.","journal-title":"Information and Control"},{"key":"1_CR27","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0019-9958(69)90631-7","volume":"15","author":"N. Zierler","year":"1969","unstructured":"N. Zierler, \u201cPrimitive trinomials whose degree is a Mersenne exponent\u201d, Information and Control, 15 (1969) pp. 67\u201369.","journal-title":"Information and Control"},{"key":"1_CR28","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1090\/S0002-9939-1958-0094332-2","volume":"9","author":"N. Zierler","year":"1958","unstructured":"N. Zierler, \u201cOn the theorem of Gleason and Marsh\u201d, Proc. Amer. Math. Soc., 9 (1958), pp. 236\u2013237.","journal-title":"Proc. Amer. Math. Soc."}],"container-title":["Lecture Notes in Computer Science","Information Theory and Applications"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-57936-2_27.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T21:15:48Z","timestamp":1605647748000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-57936-2_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994]]},"ISBN":["9783540579366","9783540483922"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/3-540-57936-2_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994]]}}}