{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T22:26:22Z","timestamp":1770071182826,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,7,25]],"date-time":"2016-07-25T00:00:00Z","timestamp":1469404800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2017,1]]},"DOI":"10.1007\/s12095-016-0199-0","type":"journal-article","created":{"date-parts":[[2016,7,24]],"date-time":"2016-07-24T22:42:42Z","timestamp":1469400162000},"page":"117-131","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Two classes of p-ary bent functions and linear codes with three or four weights"],"prefix":"10.1007","volume":"9","author":[{"given":"Guangkui","family":"Xu","sequence":"first","affiliation":[]},{"given":"Xiwang","family":"Cao","sequence":"additional","affiliation":[]},{"given":"Shanding","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,7,25]]},"reference":[{"key":"199_CR1","unstructured":"Bae, S., Li, C., Yue, Q.: Some results on two-weight and three-weight linear codes preprint, 2015."},{"key":"199_CR2","unstructured":"Carlet, C.: Two New Classes of Bent Functions. Advances in Cryptology-EUROCRYPT93, Springer, Pp. 77\u2013101 (1994)."},{"key":"199_CR3","doi-asserted-by":"crossref","unstructured":"Carlet, C.: On Bent and Highly Nonlinear Balanced\/Resilient Functions and Their Algebraic Immunities. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Springer, Pp. 1\u201328 (2006).","DOI":"10.1007\/11617983_1"},{"key":"199_CR4","first-page":"257","volume":"2","author":"C Carlet","year":"2010","unstructured":"Carlet, C.: Boolean functions for cryptography and error correcting codes. Boolean Models and Methods in Mathematics. Comput. Sci. Eng. 2, 257\u2013397 (2010).","journal-title":"Comput. Sci. Eng."},{"issue":"8","key":"199_CR5","doi-asserted-by":"crossref","first-page":"2392","DOI":"10.1016\/j.jcta.2011.06.005","volume":"118","author":"C Carlet","year":"2011","unstructured":"Carlet, C., Mesnager, S.: On Dillon\u2019s class \u210b $\\mathcal {H}$ of bent functions, Niho bent functions and o-polynomials. J. Combin. Theory Ser A. 118 (8), 2392\u20132410 (2011).","journal-title":"J. Combin. Theory Ser A"},{"issue":"2","key":"199_CR6","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s10801-010-0270-4","volume":"34","author":"YM Chee","year":"2011","unstructured":"Chee, Y. M., Tan, Y., Zhang, X. D.: Strongly regular graphs constructed from p-ary bent functions. J. Algebr. Comb. 34 (2), 251\u2013266 (2011).","journal-title":"J. Algebr. Comb."},{"key":"199_CR7","unstructured":"Dillon, J. F.: Elementary hadamard difference sets, Ph.D. thesis, University of Maryland College Park, 1974."},{"issue":"1","key":"199_CR8","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.tcs.2004.09.011","volume":"330","author":"C Ding","year":"2005","unstructured":"Ding, C., Wang, X.: A coding theory construction of new systematic authentication codes. Theoretical Comput. Sci. 330 (1), 81\u201399 (2005).","journal-title":"Theoretical Comput. Sci."},{"key":"199_CR9","doi-asserted-by":"crossref","unstructured":"Ding, C., Luo, J., Niederreiter, H.: Two Weight Codes Punctured from Irreducible Cyclic Codes. Proc. of the First International Workshop on Coding Theory and Cryptography, Singapore, World Scientific, 119-124 (2008).","DOI":"10.1142\/9789812832245_0009"},{"issue":"6","key":"199_CR10","doi-asserted-by":"crossref","first-page":"3265","DOI":"10.1109\/TIT.2015.2420118","volume":"61","author":"C Ding","year":"2015","unstructured":"Ding, C.: Linear codes from some 2-designs. IEEE Trans. Inform. Theory. 61 (6), 3265\u20133275 (2015).","journal-title":"IEEE Trans. Inform. Theory"},{"key":"199_CR11","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.disc.2015.09.001","volume":"339","author":"C Ding","year":"2016","unstructured":"Ding, C., Li, C., Li, N., Zhou, Z.: Three-weight cyclic codes and their weight distributions. Discret. Math. 339, 415\u2013427 (2016).","journal-title":"Discret. Math."},{"issue":"9","key":"199_CR12","doi-asserted-by":"crossref","first-page":"2288","DOI":"10.1016\/j.disc.2016.03.029","volume":"339","author":"C Ding","year":"2016","unstructured":"Ding, C.: A construction of binary linear codes from Boolean functions. Discret. Math. 339 (9), 2288\u20132303 (2016).","journal-title":"Discret. Math."},{"issue":"11","key":"199_CR13","first-page":"1879","volume":"18","author":"K Ding","year":"2014","unstructured":"Ding, K., Ding, C.: Binary linear codes with three weights. IEEE Trans. Inform. Theory. 18 (11), 1879\u20131882 (2014).","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"11","key":"199_CR14","doi-asserted-by":"crossref","first-page":"5835","DOI":"10.1109\/TIT.2015.2473861","volume":"61","author":"K Ding","year":"2015","unstructured":"Ding, K., Ding, C.: A class of two-weight and three-weight codes and their applications in secret sharing. IEEE Trans. Inf. Theory. 61 (11), 5835\u20135842 (2015).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"199_CR15","doi-asserted-by":"crossref","first-page":"2274","DOI":"10.1109\/TIT.2007.896886","volume":"53","author":"C Ding","year":"2007","unstructured":"Ding, C., Niederreiter, H.: Cyclotomic linear codes of order 3. IEEE Trans. Inf. Theory. 53 (6), 2274\u20132277 (2007).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"199_CR16","doi-asserted-by":"crossref","first-page":"2018","DOI":"10.1109\/TIT.2006.872854","volume":"52","author":"T Helleseth","year":"2006","unstructured":"Helleseth, T., Kholosha, A.: Monomial and quadratic bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory. 52 (5), 2018\u20132032 (2006).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9","key":"199_CR17","doi-asserted-by":"crossref","first-page":"4646","DOI":"10.1109\/TIT.2010.2055130","volume":"56","author":"T Helleseth","year":"2010","unstructured":"Helleseth, T., Kholosha, A.: New binomial bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory. 56 (9), 4646\u20134652 (2010).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9","key":"199_CR18","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1109\/LCOMM.2015.2455032","volume":"19","author":"Z Heng","year":"2015","unstructured":"Heng, Z., Yue, Q.: A class of binary linear codes with at most three weights. IEEE Commun. Lett. 19 (9), 1488\u20131491 (2015).","journal-title":"IEEE Commun. Lett."},{"key":"199_CR19","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.ffa.2015.12.002","volume":"38","author":"Z Heng","year":"2016","unstructured":"Heng, Z., Yue, Q.: Two classes of two-weight linear codes. Finite Fields Appl. 38, 72\u201392 (2016).","journal-title":"Finite Fields Appl."},{"issue":"4","key":"199_CR20","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.ffa.2003.12.004","volume":"10","author":"X Hou","year":"2004","unstructured":"Hou, X.: D.: p-Ary and q-ary versions of certain results about bent functions and resilient functions. Finite Fields Appl. 10 (4), 566\u2013582 (2004).","journal-title":"Finite Fields Appl."},{"key":"199_CR21","doi-asserted-by":"crossref","unstructured":"Huffman, W. C., Pless, V.: Fundamentals of Error-Correcting codes cambridge, U.K.: Cambridge univ press, 2003.","DOI":"10.1017\/CBO9780511807077"},{"issue":"9","key":"199_CR22","doi-asserted-by":"crossref","first-page":"6054","DOI":"10.1109\/TIT.2012.2199736","volume":"58","author":"W Jia","year":"2012","unstructured":"Jia, W., Zeng, X., Helleseth, T., Li, C.: A class of binomial bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory. 58 (9), 6054\u20136063 (2012).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"199_CR23","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0097-3165(85)90049-4","volume":"40","author":"PV Kumar","year":"1985","unstructured":"Kumar, P. V., Scholtz, R. A., Welch, L. R.: Generalized bent functions and their properties. J. Combin. Theory Ser A. 40 (1), 90\u2013107 (1985).","journal-title":"J. Combin. Theory Ser A"},{"issue":"2","key":"199_CR24","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.ffa.2015.02.007","volume":"34","author":"C Li","year":"2015","unstructured":"Li, C., Yue, Q.: A class of cyclic codes from two distinct fnite felds codes. Finite Fields Appl. 34 (2), 305\u2013316 (2015).","journal-title":"Finite Fields Appl."},{"issue":"7","key":"199_CR25","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1109\/TIT.2014.2317785","volume":"60","author":"C Li","year":"2014","unstructured":"Li, C., Yue, Q., Li, F.: Hamming weights of the duals of cyclic codes with two zeros. IEEE Trans. Inf. Theory. 60 (7), 3895\u20133902 (2014).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"199_CR26","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1109\/TIT.2012.2229782","volume":"59","author":"N Li","year":"2013","unstructured":"Li, N., Helleseth, T., Tang, X., Kholosha, A.: Several new classes of bent functions from Dillon exponents. IEEE Trans. Inf. Theory. 59 (3), 1818\u20131831 (2013).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"199_CR27","volume-title":"Finite Fields","author":"R Lidl","year":"1983","unstructured":"Lidl, R., Niederrreiter, H.: Finite Fields. Addison-Wesley, London (1983)."},{"issue":"7","key":"199_CR28","doi-asserted-by":"crossref","first-page":"4397","DOI":"10.1109\/TIT.2014.2320974","volume":"60","author":"S Mesnager","year":"2014","unstructured":"Mesnager, S.: Several new infinite families of bent functions and their duals. IEEE Trans. Inf. Theory. 60 (7), 4397\u20134407 (2014).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"199_CR29","unstructured":"Mesnager, S.: Bent functions: fundamentals and results. Springer, New York. to appear."},{"issue":"3","key":"199_CR30","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/0097-3165(76)90024-8","volume":"20","author":"OS Rothaus","year":"1976","unstructured":"Rothaus, O. S.: On bent functions. J. Combin. Theory Ser A. 20 (3), 300\u2013305 (1976).","journal-title":"J. Combin. Theory Ser A"},{"issue":"6","key":"199_CR31","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1016\/j.jcta.2009.05.003","volume":"117","author":"Y Tan","year":"2010","unstructured":"Tan, Y., Pott, A., Feng, T.: Strongly regular graphs associated with ternary bent functions. J. Combin. Theory Ser A. 117 (6), 668\u2013682 (2010).","journal-title":"J. Combin. Theory Ser A"},{"issue":"3","key":"199_CR32","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1109\/TIT.2016.2518678","volume":"62","author":"C Tang","year":"2016","unstructured":"Tang, C., Li, N., Qi, F., Zhou, Z., Helleseth, T.: Linear codes with two or three weights from weakly regular bent functions. IEEE Trans. Inf. Theory. 62 (3), 1166\u20131176 (2016).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"199_CR33","doi-asserted-by":"publisher","unstructured":"Xiang, C.: Linear codes from a generic construction. Cryptogr. Commun. (2015). doi: 10.1007\/s12095-015-0158-1 .","DOI":"10.1007\/s12095-015-0158-1"},{"issue":"1","key":"199_CR34","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s12095-015-0145-6","volume":"8","author":"G Xu","year":"2016","unstructured":"Xu, G., Cao, X., Xu, S.: Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method. Cryptogr Commun. 8 (1), 155\u2013171 (2016).","journal-title":"Cryptogr Commun."},{"issue":"2","key":"199_CR35","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/TIT.2005.862125","volume":"52","author":"J Yuan","year":"2006","unstructured":"Yuan, J., Carlet, C., Ding, C.: The weight distribution of a class of linear codes from perfect nonlinear functions. IEEE Trans. Inf. Theory. 52 (2), 712\u2013717 (2006).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"199_CR36","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.ffa.2009.12.001","volume":"16","author":"X Zeng","year":"2010","unstructured":"Zeng, X., Hu, L., Jiang, W., Yue, Q., Cao, X.: The weight distribution of a class of p-ary cyclic codes. Finite Fields Appl. 16 (1), 56\u201373 (2010).","journal-title":"Finite Fields Appl."},{"key":"199_CR37","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.ffa.2013.08.005","volume":"25","author":"Z Zhou","year":"2014","unstructured":"Zhou, Z., Ding, C.: A class of three-weight cyclic codes. Finite Fields Appl. 25, 79\u201393 (2014).","journal-title":"Finite Fields Appl."},{"key":"199_CR38","doi-asserted-by":"publisher","unstructured":"Zhou, Z., Li, N., Fan, C., Helleseth, T.: Linear codes with two or three weights from quadratic bent functions. Des. Codes Cryptogr. (2015). doi: 10.1007\/s10623-015-0144-9 .","DOI":"10.1007\/s10623-015-0144-9"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-016-0199-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12095-016-0199-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-016-0199-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-016-0199-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T15:05:06Z","timestamp":1498316706000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12095-016-0199-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,25]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["199"],"URL":"https:\/\/doi.org\/10.1007\/s12095-016-0199-0","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,25]]}}}