{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T08:36:21Z","timestamp":1776760581911,"version":"3.51.2"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1990,3,1]],"date-time":"1990-03-01T00:00:00Z","timestamp":636249600000},"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":[[1990,3]]},"DOI":"10.1007\/bf01810846","type":"journal-article","created":{"date-parts":[[2005,6,27]],"date-time":"2005-06-27T19:33:01Z","timestamp":1119900781000},"page":"43-53","source":"Crossref","is-referenced-by-count":52,"title":["On the construction of irreducible self-reciprocal polynomials over finite fields"],"prefix":"10.1007","volume":"1","author":[{"given":"Helmut","family":"Meyn","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF01810846_CR1","first-page":"255","volume":"28","author":"G. E. Andrews","year":"1985","unstructured":"Andrews, G. E.: Reciprocal polynomials and quadratic transformations. Utilitas Math.28, 255\u2013264 (1985)","journal-title":"Utilitas Math."},{"key":"BF01810846_CR2","doi-asserted-by":"crossref","unstructured":"Berlekamp, E. R.: Bit-serial Reed-Solomon encoders. IEEE Trans. Inform. TheoryIT-28, 869\u2013874 (1982)","DOI":"10.1109\/TIT.1982.1056591"},{"key":"BF01810846_CR3","doi-asserted-by":"crossref","DOI":"10.1090\/conm\/095","volume-title":"Infinite algebraic extensions of finite fields. Contemporary Mathematics, vol.95","author":"J. V. Brawley","year":"1989","unstructured":"Brawley, J. V., Schnibben, G. E.: Infinite algebraic extensions of finite fields. Contemporary Mathematics, vol.95, American Math. Soc., Providence, Rhode Island 1989"},{"key":"BF01810846_CR4","first-page":"212","volume":"227","author":"L. Carlitz","year":"1967","unstructured":"Carlitz, L.: Some theorems on irreducible reciprocal polynomials over a finite field. J. Reine Angew. Math.227, 212\u2013220 (1967)","journal-title":"J. Reine Angew. Math."},{"key":"BF01810846_CR5","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1017\/S0305004100045023","volume":"66","author":"S. D. Cohen","year":"1969","unstructured":"Cohen, S. D.: On irreducible polynomials of certain types in finite fields. Proc. Camb. Phil. Soc.66, 335\u2013344 (1969)","journal-title":"Proc. Camb. Phil. Soc."},{"key":"BF01810846_CR6","first-page":"83","volume":"24","author":"S. D. Cohen","year":"1987","unstructured":"Cohen, S. D.: Polynomials over finite fields with large order and level. Bull. Korean Math. Soc.24, 83\u201396 (1987)","journal-title":"Bull. Korean Math. Soc."},{"key":"BF01810846_CR7","first-page":"117","volume":"22","author":"D. Garbe","year":"1985","unstructured":"Garbe, D.: On the level of irreducible polynomials over Galois fields. J. Korean Math. Soc.22, 117\u2013124 (1985)","journal-title":"J. Korean Math. Soc."},{"key":"BF01810846_CR8","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1215\/ijm\/1255631587","volume":"5","author":"E. N. Gilbert","year":"1961","unstructured":"Gilbert, E. N., Riordan, J.: Symmetry types of periodic sequences. Illinois J. Math.5, 657\u2013665 (1961)","journal-title":"Illinois J. Math."},{"key":"BF01810846_CR9","unstructured":"G\u00f6tz, W.: Selbstreziproke Polynome \u00fcber endlichen K\u00f6rpern. Diploma thesis, Erlangen (1989)"},{"key":"BF01810846_CR10","doi-asserted-by":"crossref","unstructured":"Hong, S. J., Bossen, D. C.: On some properties of self-reciprocal polynomials. IEEE Trans. Inform. TheoryIT-21 462\u2013464 (1975)","DOI":"10.1109\/TIT.1975.1055396"},{"key":"BF01810846_CR11","volume-title":"Finite Fields. Encyclopedia of Mathematics and its Applications, vol. 20","author":"R. Lidl","year":"1983","unstructured":"Lidl, R., Niederreiter, H.: Finite Fields. Encyclopedia of Mathematics and its Applications, vol. 20, Reading, MA: Addison-Wesley 1983"},{"key":"BF01810846_CR12","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. Amsterdam: North-Holland 1977"},{"key":"BF01810846_CR13","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/S0019-9958(64)90438-3","volume":"7","author":"J. L. Massey","year":"1964","unstructured":"Massey, J. L.: Reversible codes. Information Control7, 369\u2013380 (1964)","journal-title":"Information Control"},{"key":"BF01810846_CR14","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0012-365X(78)90043-2","volume":"22","author":"R. L. Miller","year":"1978","unstructured":"Miller, R. L.: Necklaces, Symmetries and Self-Reciprocal Polynomials. Discrete Math.22, 25\u201333 (1978)","journal-title":"Discrete Math."},{"key":"BF01810846_CR15","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1147\/rd.186.0579","volume":"18","author":"A. M. Patel","year":"1974","unstructured":"Patel, A. M., Hong, S. J.: Optimal rectangular code for high density magnetic tapes. IBM J. Res. Develop.18, 579\u2013588 (1974)","journal-title":"IBM J. Res. Develop."},{"key":"BF01810846_CR16","first-page":"403","volume":"13","author":"R. R. Varshamov","year":"1969","unstructured":"Varshamov, R. R., Garakov, G. A.: On the Theory of Selfdual Polynomials over a Galois Field (Russian). Bull. Math. Soc. Sci. Math. R. S. Roumanie, (N.S.)13, 403\u2013415 (1969)","journal-title":"Bull. Math. Soc. Sci. Math. R. S. Roumanie, (N.S.)"},{"key":"BF01810846_CR17","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1080\/00150517.1988.12429608","volume":"26","author":"D. Wiedemann","year":"1988","unstructured":"Wiedemann, D.: An Iterated Quadratic Extension of GF(2). Fibonacci Quart.26, 290\u2013295 (1988)","journal-title":"Fibonacci Quart."}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01810846.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01810846\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01810846","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T23:26:16Z","timestamp":1735773976000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01810846"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,3]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,3]]}},"alternative-id":["BF01810846"],"URL":"https:\/\/doi.org\/10.1007\/bf01810846","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,3]]}}}