{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:02:55Z","timestamp":1772283775332,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,8,31]],"date-time":"2018-08-31T00:00:00Z","timestamp":1535673600000},"content-version":"tdm","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":["Cryptogr. Commun."],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s12095-018-0324-3","type":"journal-article","created":{"date-parts":[[2018,8,31]],"date-time":"2018-08-31T03:28:25Z","timestamp":1535686105000},"page":"735-757","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Binary sequences with period N and nonlinear complexity N \u2212\u20092"],"prefix":"10.1007","volume":"11","author":[{"given":"Zibi","family":"Xiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8351-8766","authenticated-orcid":false,"given":"Xiangyong","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoyun","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yupeng","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,8,31]]},"reference":[{"issue":"4","key":"324_CR1","doi-asserted-by":"publisher","first-page":"822","DOI":"10.1109\/18.53741","volume":"36","author":"AH Chan","year":"1990","unstructured":"Chan, A.H., Games, R.A.: On the quadratic spans of DeBruijn sequences. IEEE Trans. Inf. Theory 36(4), 822\u2013829 (1990)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"324_CR2","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":"3","key":"324_CR3","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"},{"issue":"3","key":"324_CR4","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1023\/A:1008295603824","volume":"10","author":"D Erdmann","year":"1997","unstructured":"Erdmann, D., Murphy, S.: An approximate distribution for the maximum order complexity. Des. Codes Cryptogr. 10(3), 325\u2013339 (1997)","journal-title":"Des. Codes Cryptogr."},{"key":"324_CR5","unstructured":"Jansen, C.J.A.: Investigations on nonlinear streamcipher systems: Construction and evaluation methods, Ph.D dissertation (1989)"},{"key":"324_CR6","doi-asserted-by":"crossref","unstructured":"Jansen, C.J.A., Boekee, D.E.: The shortest feedback shift register that can generate a given sequence. In: Brassard, G (ed.) Advances in Cryptology-CRYPTO\u201989, Lecture Notes in Computer Science, vol. 435, pp. 90\u201399. Springer-Verlag, New York (1989)","DOI":"10.1007\/0-387-34805-0_10"},{"issue":"5","key":"324_CR7","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"},{"issue":"11","key":"324_CR8","doi-asserted-by":"publisher","first-page":"3047","DOI":"10.1109\/TIT.2003.818400","volume":"49","author":"N Kolokotronis","year":"2003","unstructured":"Kolokotronis, N., Kalouptsidis, N.: On the linear complexity of nonlinear filtered PN-sequences. IEEE Trans. Inf. Theory 49(11), 3047\u20133059 (2003)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"324_CR9","unstructured":"Lam, C., Gong, G.: A lower bound for the linear span of filtering sequences. In State of the Art of Stream Ciphers (SASC), pp. 220\u2013233 (2004)"},{"issue":"11","key":"324_CR10","doi-asserted-by":"publisher","first-page":"7597","DOI":"10.1109\/TIT.2011.2159575","volume":"57","author":"N Li","year":"2011","unstructured":"Li, N., Tang, X.: On the linear complexity of binary sequences of period 4N with optimal autocorrelation value\/magnitude. IEEE Trans. Inf. Theory 57(11), 7597\u20137604 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"324_CR11","doi-asserted-by":"publisher","first-page":"4293","DOI":"10.1109\/TIT.2007.907442","volume":"53","author":"K Limniotis","year":"2007","unstructured":"Limniotis, K., Kolokotronis, N., Kalouptsidis, N.: On the nonlinear complexity and Lempel-Ziv complexity of finite length sequences. IEEE Trans. Inf. Theory 53(11), 4293\u20134302 (2007)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"324_CR12","doi-asserted-by":"publisher","first-page":"7646","DOI":"10.1109\/TIT.2017.2736545","volume":"63","author":"Y Luo","year":"2017","unstructured":"Luo, Y., Xing, C., You, L.: Construction of sequences with high nonlinear complexity from function fields. IEEE Trans. Inf. Theory 63(12), 7646\u20137650 (2017)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"324_CR13","unstructured":"Menezes, A.J., Van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press (1996)"},{"key":"324_CR14","doi-asserted-by":"crossref","unstructured":"Niederreiter, H.: Linear complexity and related complexity measures for sequences. In: Johansson, T., Maitra, S. (eds.) International Conference on Cryptology in India, INDOCRYPT 2003. Lecture Notes in Computer Science, vol. 2904, pp. 1\u201317. Springer, Berlin (2003)","DOI":"10.1007\/978-3-540-24582-7_1"},{"issue":"10","key":"324_CR15","doi-asserted-by":"publisher","first-page":"6696","DOI":"10.1109\/TIT.2014.2343225","volume":"60","author":"H Niederreiter","year":"2014","unstructured":"Niederreiter, H., Xing, C.: Sequences with high nonlinear complexity. IEEE Trans. Inf. Theory 60(10), 6696\u20136701 (2014)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"324_CR16","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1023\/A:1008256920596","volume":"14","author":"KG Paterson","year":"1998","unstructured":"Paterson, K.G.: Root counting, the DFT and the DFT and the linear complexity of nonlinear filtering. Des. Codes Cryptogr. 14(3), 247\u2013259 (1998)","journal-title":"Des. Codes Cryptogr."},{"issue":"1","key":"324_CR17","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10623-008-9178-6","volume":"49","author":"G Petrides","year":"2008","unstructured":"Petrides, G., Mykkeltveit, J.: Composition of recursions and nonlinear complexity of periodic binary sequences. Des. Codes Cryptogr. 49(1), 251\u2013264 (2008)","journal-title":"Des. Codes Cryptogr."},{"issue":"4","key":"324_CR18","doi-asserted-by":"publisher","first-page":"1555","DOI":"10.1109\/TIT.2005.844090","volume":"51","author":"P Rizomiliotis","year":"2005","unstructured":"Rizomiliotis, P., Kalouptsidis, N.: Results on the nonlinear span of binary sequences. IEEE Trans. Inf. Theory 51(4), 1555\u20131563 (2005)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"324_CR19","doi-asserted-by":"publisher","first-page":"1840","DOI":"10.1109\/TIT.2005.846428","volume":"51","author":"P Rizomiliotis","year":"2005","unstructured":"Rizomiliotis, P., Kolokotronis, N., Kalouptsidis, N.: On the quadratic span of binary sequences. IEEE Trans. Inf. Theory 51(5), 1840\u20131848 (2005)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9","key":"324_CR20","doi-asserted-by":"publisher","first-page":"4257","DOI":"10.1109\/TIT.2006.880054","volume":"52","author":"P Rizomiliotis","year":"2006","unstructured":"Rizomiliotis, P.: Constructing periodic binary sequences with maximum nonlinear span. IEEE Trans. Inf. Theory 52(9), 4257\u20134261 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"324_CR21","doi-asserted-by":"publisher","first-page":"6188","DOI":"10.1109\/TIT.2017.2714681","volume":"63","author":"Z Sun","year":"2017","unstructured":"Sun, Z., Zeng, X., Li, C., Helleseth, T.: Investigations on periodic sequences with maximum nonlinear complexity. IEEE Trans. Inf. Theory 63(10), 6188\u20136198 (2017)","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-018-0324-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12095-018-0324-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-018-0324-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T12:37:52Z","timestamp":1568983072000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12095-018-0324-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,31]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["324"],"URL":"https:\/\/doi.org\/10.1007\/s12095-018-0324-3","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,31]]},"assertion":[{"value":"3 December 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 August 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}