{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:59:03Z","timestamp":1772283543243,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2017,9,4]],"date-time":"2017-09-04T00:00:00Z","timestamp":1504483200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61472120"],"award-info":[{"award-number":["61472120"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2018,7]]},"DOI":"10.1007\/s10623-017-0408-7","type":"journal-article","created":{"date-parts":[[2017,9,4]],"date-time":"2017-09-04T07:41:19Z","timestamp":1504510879000},"page":"1483-1497","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["New generalized cyclotomic binary sequences of period $$p^2$$ p 2"],"prefix":"10.1007","volume":"86","author":[{"given":"Zibi","family":"Xiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangyong","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunlei","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tor","family":"Helleseth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,4]]},"reference":[{"key":"408_CR1","volume-title":"Introduction to Analytic Number Theory","author":"TM Apostol","year":"1976","unstructured":"Apostol T.M.: Introduction to Analytic Number Theory. Springer, New York (1976)."},{"issue":"5","key":"408_CR2","doi-asserted-by":"publisher","first-page":"1849","DOI":"10.1109\/TIT.2005.846450","volume":"51","author":"E Bai","year":"2005","unstructured":"Bai E., Liu X., Xiao G.: Linear complexity of new generalized cyclotomic sequences of order two of length $$pq$$ p q . IEEE Trans. Inf. Theory 51(5), 1849\u20131853 (2005).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"408_CR3","volume-title":"Stream Ciphers and Number Theory","author":"TW Cusick","year":"1998","unstructured":"Cusick T.W., Ding C., Renvall A.: Stream Ciphers and Number Theory. Elsevier Science B.V, Amsterdam (1998)."},{"issue":"2","key":"408_CR4","doi-asserted-by":"publisher","first-page":"97","DOI":"10.4064\/aa103-2-1","volume":"103","author":"J Cassaigne","year":"2002","unstructured":"Cassaigne J., Mauduit C., S\u00e1rk\u00f6zy A.: On finite pseudorandom binary sequences VII: the measure of pseudorandomness of pseudorandomness. Acta Arith. 103(2), 97\u2013118 (2002).","journal-title":"Acta Arith."},{"key":"408_CR5","doi-asserted-by":"crossref","unstructured":"Ding C.: Binary cyclotomic generators. Fast Software Encryption. Lecture Notes in Computer Science, vol. 1008, pp. 29\u201360. Springer, Leuven (1995).","DOI":"10.1007\/3-540-60590-8_4"},{"key":"408_CR6","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1006\/ffta.1997.0181","volume":"3","author":"C Ding","year":"1997","unstructured":"Ding C.: Linear complexity of generalized cyclotomic binary sequences of order 2. Finite Fields Appl. 3, 159\u2013174 (1997).","journal-title":"Finite Fields Appl."},{"issue":"4","key":"408_CR7","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1142\/S021819679800020X","volume":"08","author":"C Ding","year":"1998","unstructured":"Ding C.: Linear complexity of some generalized cyclotomic sequences. Int. J. Algebra Comput. 08(4), 431\u2013442 (1998).","journal-title":"Int. J. Algebra Comput."},{"issue":"3","key":"408_CR8","doi-asserted-by":"publisher","first-page":"1276","DOI":"10.1109\/18.669398","volume":"44","author":"C Ding","year":"1998","unstructured":"Ding C., Helleseth T., Shan W.: On the linear complexity of Legendre sequences. IEEE Trans. Inf. Theory 44(3), 1276\u20131278 (1998).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"408_CR9","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1006\/ffta.1998.0207","volume":"4","author":"C Ding","year":"1998","unstructured":"Ding C., Helleseth T.: New generalized cyclotomy and its applications. Finite Fields Appl. 4, 140\u2013166 (1998).","journal-title":"Finite Fields Appl."},{"issue":"2","key":"408_CR10","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1109\/18.748996","volume":"45","author":"C Ding","year":"1999","unstructured":"Ding C., Helleseth T.: Generalized cyclotomy codes of length $$p_1^{m_1}p_2^{m_2} \\ldots p_t^{m_t}$$ p 1 m 1 p 2 m 2 \u2026 p t m t . IEEE Trans. Inf. Theory 45(2), 467\u2013474 (1999).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"408_CR11","doi-asserted-by":"publisher","first-page":"2606","DOI":"10.1109\/18.796414","volume":"45","author":"C Ding","year":"1999","unstructured":"Ding C., Helleseth T., Lam K.Y.: Several classes of binary sequences with three-level autocorrelation. IEEE Trans. Inf. Theory 45(7), 2606\u20132612 (1999).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"408_CR12","unstructured":"Dorais F.G., Klyve D.: A Wieferich prime search up to $$6.7\\times 10^{15}$$ 6.7 \u00d7 10 15 . J. Integer Seq. 14(9), (2011). https:\/\/cs.uwaterloo.ca\/journals\/JIS\/VOL14\/Klyve\/klyve3.html"},{"key":"408_CR13","doi-asserted-by":"publisher","first-page":"784","DOI":"10.1016\/j.ins.2012.07.048","volume":"222","author":"X Du","year":"2013","unstructured":"Du X., Chen Z.: A generalization of the Hall\u2019s sextic residue sequences. Inf. Sci. 222, 784\u2013794 (2013).","journal-title":"Inf. Sci."},{"issue":"2","key":"408_CR14","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1109\/TIT.2013.2290694","volume":"60","author":"C Fan","year":"2014","unstructured":"Fan C., Ge G.: A unified approach to Whiteman\u2019s and Ding-Helleseth\u2019s generalized cyclotomy over residue class ring. IEEE Trans. Inf. Theory 60(2), 1326\u20131336 (2014).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"408_CR15","doi-asserted-by":"publisher","first-page":"5534","DOI":"10.1109\/TIT.2012.2196254","volume":"58","author":"L Hu","year":"2012","unstructured":"Hu L., Yue Q., Wang M.: The linear complexity of Whiteman\u2019s generalized cyclotomic sequences of period $$p^{m+1}q^{n+1}$$ p m + 1 q n + 1 . IEEE Trans. Inf. Theory 58(8), 5534\u20135543 (2012).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"408_CR16","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s10623-012-9610-9","volume":"67","author":"P Ke","year":"2013","unstructured":"Ke P., Zhang J., Zhang S.: On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length $$2p^m$$ 2 p m . Des. Codes Cryptogr. 67(3), 325\u2013339 (2013).","journal-title":"Des. Codes Cryptogr."},{"issue":"5","key":"408_CR17","doi-asserted-by":"publisher","first-page":"2094","DOI":"10.1109\/18.930950","volume":"47","author":"JH Kim","year":"2001","unstructured":"Kim J.H., Song H.Y.: On the linear complexity of Hall\u2019s sextic residue sequences. IEEE Trans. Inf. Theory 47(5), 2094\u20132096 (2001).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"408_CR18","doi-asserted-by":"crossref","unstructured":"Kim Y.J., Jin S.Y., Song H.Y.: Linear complexity and autocorrelation of prime cube sequences. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Lecture Notes in Computer Science, vol. 4851, pp. 188\u2013197. Springer, Berlin (2007).","DOI":"10.1007\/978-3-540-77224-8_23"},{"issue":"4","key":"408_CR19","doi-asserted-by":"publisher","first-page":"365","DOI":"10.4064\/aa-82-4-365-377","volume":"82","author":"C Mauduit","year":"1997","unstructured":"Mauduit C., S\u00e1rk\u00f6zy A.: On finite pseudorandom binary sequences I: measure of pseudorandomness, the Legendre symbol. Acta Arith. 82(4), 365\u2013377 (1997).","journal-title":"Acta Arith."},{"key":"408_CR20","unstructured":"Niederreiter H.: Linear complexity and related complexity measures for sequences. Progress in Cryptology-INDOCRYPT. Lecture Notes in Computer Science, vol. 2904, pp. 1\u201317. Springer, Berlin (2003)."},{"issue":"1","key":"408_CR21","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1137\/0112010","volume":"12","author":"RJ Turyn","year":"1964","unstructured":"Turyn R.J.: The linear generation of the Legendre sequence. J. Soc. Ind. Appl. Math. 12(1), 115\u2013116 (1964).","journal-title":"J. Soc. Ind. Appl. Math."},{"issue":"1","key":"408_CR22","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1215\/ijm\/1255631810","volume":"6","author":"AL Whiteman","year":"1962","unstructured":"Whiteman A.L.: A family of difference sets. Illionis J. Math. 6(1), 107\u2013121 (1962).","journal-title":"Illionis J. Math."},{"issue":"4","key":"408_CR23","doi-asserted-by":"publisher","first-page":"1078","DOI":"10.1016\/j.ins.2007.02.040","volume":"178","author":"T Yan","year":"2008","unstructured":"Yan T., Huang B., Xiao G.: Cryptographic properties of some binary generalized cyclotomic sequences with the length $$p^2$$ p 2 . Inf. Sci. 178(4), 1078\u20131086 (2008).","journal-title":"Inf. Sci."},{"issue":"2","key":"408_CR24","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/j.aml.2007.03.011","volume":"21","author":"T Yan","year":"2008","unstructured":"Yan T., Li S., Xiao G.: On the linear complexity of generalized cyclotomic sequences with the period $$p^m$$ p m . Appl. Math. Lett. 21(2), 187\u2013193 (2008).","journal-title":"Appl. Math. Lett."},{"issue":"5","key":"408_CR25","doi-asserted-by":"publisher","first-page":"3237","DOI":"10.1109\/TIT.2013.2237754","volume":"59","author":"X Zeng","year":"2013","unstructured":"Zeng X., Cai H., Tang X., Yang Y.: Optimal frequency hopping sequences of odd length. IEEE Trans. Inf. Theory 59(5), 3237\u20133248 (2013).","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-017-0408-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-017-0408-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-017-0408-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,2]],"date-time":"2019-10-02T23:33:37Z","timestamp":1570059217000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-017-0408-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,4]]},"references-count":25,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["408"],"URL":"https:\/\/doi.org\/10.1007\/s10623-017-0408-7","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,4]]}}}