{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:28:37Z","timestamp":1764174517828},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,5,29]],"date-time":"2018-05-29T00:00:00Z","timestamp":1527552000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s00200-018-0361-3","type":"journal-article","created":{"date-parts":[[2018,5,29]],"date-time":"2018-05-29T06:48:58Z","timestamp":1527576538000},"page":"93-106","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Several classes of binary linear codes and their weight enumerators"],"prefix":"10.1007","volume":"30","author":[{"given":"Fei","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiuyan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tongjiang","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,5,29]]},"reference":[{"issue":"2","key":"361_CR1","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1137\/0404016","volume":"4","author":"IF Blake","year":"1991","unstructured":"Blake, I.F., Kith, K.: On the complete weight enumerator of Reed\u2013Solomon codes. SIAM J. Disc. Math. 4(2), 164\u2013171 (1991)","journal-title":"SIAM J. Disc. Math."},{"key":"361_CR2","doi-asserted-by":"publisher","first-page":"5","DOI":"10.7146\/math.scand.a-11793","volume":"44","author":"L Carlitz","year":"1979","unstructured":"Carlitz, L.: Exolicite evaluation of certain exponential sums. Math. Scand. 44, 5\u201316 (1979)","journal-title":"Math. Scand."},{"key":"361_CR3","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1002\/mana.19800960125","volume":"96","author":"L Carlitz","year":"1980","unstructured":"Carlitz, L.: Evaluation of some exponential sums over a finite field. Math. Nachr. 96, 319\u2013339 (1980)","journal-title":"Math. Nachr."},{"key":"361_CR4","doi-asserted-by":"publisher","first-page":"241","DOI":"10.4064\/aa-83-3-241-251","volume":"83","author":"RS Coulter","year":"1998","unstructured":"Coulter, R.S.: Explicit evaluation of some Weil sums. Acta Arith. 83, 241\u2013251 (1998)","journal-title":"Acta Arith."},{"key":"361_CR5","first-page":"171","volume":"28","author":"RS Coulter","year":"1999","unstructured":"Coulter, R.S.: On the evaluation of a class of Weil sums in characteristic 2. N. Z. J. Math. 28, 171\u2013184 (1999)","journal-title":"N. Z. J. Math."},{"key":"361_CR6","doi-asserted-by":"crossref","unstructured":"Choi, S.T., Kim, J.Y., No, J.S., Chung, H.: Weight distribution of some cyclic codes. In: Proceedings of the International Symposium on Information Theory, pp. 2911\u20132913 (2012)","DOI":"10.1109\/ISIT.2012.6284056"},{"key":"361_CR7","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0012-365X(84)90047-5","volume":"50","author":"B Courteau","year":"1984","unstructured":"Courteau, B., Wolfmann, J.: On triple-sum-sets and two or three weights codes. Discrete Math. 50, 179\u2013191 (1984)","journal-title":"Discrete Math."},{"key":"361_CR8","unstructured":"Ding, C.: A class of three-weight and four-weight codes. In: Xing, C., et al. (eds.) Proceedings of the Second International Workshop on Coding Theory and Cryptography, Lecture Notes in Computer Science. Springer, vol. 5557, pp. 34\u201342(2009)"},{"issue":"6","key":"361_CR9","doi-asserted-by":"publisher","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. Inf. Theory 61(6), 3265\u20133275 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"361_CR10","doi-asserted-by":"publisher","first-page":"1879","DOI":"10.1109\/LCOMM.2014.2361516","volume":"18","author":"K Ding","year":"2014","unstructured":"Ding, K., Ding, C.: Bianry linear codes with three weights. IEEE Commun. Lett. 18(11), 1879\u20131882 (2014)","journal-title":"IEEE Commun. Lett."},{"issue":"11","key":"361_CR11","doi-asserted-by":"publisher","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":"12","key":"361_CR12","doi-asserted-by":"publisher","first-page":"7940","DOI":"10.1109\/TIT.2013.2281205","volume":"59","author":"C Ding","year":"2013","unstructured":"Ding, C., Gao, Y., Zhou, Z.: Five families of three-weight ternary cyclic codes and their duals. IEEE Trans. Inf. Theory 59(12), 7940\u20137946 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"361_CR13","doi-asserted-by":"publisher","first-page":"8000","DOI":"10.1109\/TIT.2011.2165314","volume":"57","author":"C Ding","year":"2011","unstructured":"Ding, C., Liu, Y., Ma, C., Zeng, L.: The weight distributions of the duals of cyclic codes with two zeros. IEEE Trans. Inf. Theory 57(12), 8000\u20138006 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"361_CR14","first-page":"119","volume-title":"Proceedings of the First Worshop on Coding and Cryptography","author":"C Ding","year":"2008","unstructured":"Ding, C., Luo, J., Niederreiter, H.: Two-weight codes punctured from irreducible cyclic codes. In: Li, Y., et al. (eds.) Proceedings of the First Worshop on Coding and Cryptography, pp. 119\u2013124. World Scientific, Singapore (2008)"},{"issue":"2","key":"361_CR15","doi-asserted-by":"publisher","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. Disctrete Math. 339(2), 415\u2013427 (2016)","journal-title":"Disctrete Math."},{"issue":"4","key":"361_CR16","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1016\/j.disc.2012.11.009","volume":"313","author":"C Ding","year":"2013","unstructured":"Ding, C., Yang, J.: Hamming weights in irreducible cyclic codes. Discrete Math. 313(4), 434\u2013446 (2013)","journal-title":"Discrete Math."},{"issue":"6","key":"361_CR17","doi-asserted-by":"publisher","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 \n                    \n                      \n                    \n                    $$3$$\n                    \n                      \n                        \n                          3\n                        \n                      \n                    \n                  . IEEE Trans. Inf. Theory 53(6), 2274\u20132277 (2007)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"361_CR18","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s00200-017-0319-x","volume":"28","author":"X Du","year":"2017","unstructured":"Du, X., Wan, Y.: Linear codes from quadratic forms. Appl. Algebra Eng. Commun. Comput. 28(6), 535\u2013547 (2017)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"361_CR19","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s10623-011-9514-0","volume":"62","author":"T Feng","year":"2012","unstructured":"Feng, T.: On cyclic codes of length \n                    \n                      \n                    \n                    $$2^{2^r}-1$$\n                    \n                      \n                        \n                          \n                            2\n                            \n                              2\n                              r\n                            \n                          \n                          -\n                          1\n                        \n                      \n                    \n                   with two zeros whose dual codes have three weights. Des. Codes Cryptogr. 62, 253\u2013258 (2012)","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"361_CR20","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1016\/j.ffa.2007.03.003","volume":"14","author":"K Feng","year":"2008","unstructured":"Feng, K., Luo, J.: Weight distribution of some reducible cyclic codes. Finite Fields Appl. 14(2), 390\u2013409 (2008)","journal-title":"Finite Fields Appl."},{"issue":"7","key":"361_CR21","doi-asserted-by":"publisher","first-page":"1403","DOI":"10.1007\/s11425-013-4668-z","volume":"56","author":"T Feng","year":"2012","unstructured":"Feng, T., Leung, K., Xiang, Q.: Binary cyclic codes with two primitive nonzeros. Sci. China Math. 56(7), 1403\u20131412 (2012)","journal-title":"Sci. China Math."},{"key":"361_CR22","doi-asserted-by":"publisher","first-page":"843","DOI":"10.1016\/j.ffa.2006.09.009","volume":"13","author":"X Hou","year":"2007","unstructured":"Hou, X.: Explicit evaluation of certain exponential sums of binary quadratic functions. Finite Fields Appl. 13, 843\u2013868 (2007)","journal-title":"Finite Fields Appl."},{"key":"361_CR23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807077","volume-title":"Fundamentals of Error-Correcting Codes","author":"WC Huffman","year":"2003","unstructured":"Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)"},{"key":"361_CR24","unstructured":"Kith, K.: Complete weight enumeration of Reed-Solomon codes, Masters thesis, Department of Electrical and Computing Engineering, University of Waterloo, Waterloo, Ontario, Canada (1989)"},{"issue":"12","key":"361_CR25","doi-asserted-by":"publisher","first-page":"5332","DOI":"10.1109\/TIT.2008.2006424","volume":"54","author":"J Luo","year":"2008","unstructured":"Luo, J., Feng, K.: On the weight distribution of two classes of cyclic codes. IEEE Trans. Inf. Theory 54(12), 5332\u20135344 (2008)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"361_CR26","doi-asserted-by":"publisher","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"},{"key":"361_CR27","volume-title":"Finite Fields","author":"R Lidl","year":"1997","unstructured":"Lidl, R., Niederreiter, H.: Finite Fields. Cambridge University Press, New York (1997)"},{"issue":"2","key":"361_CR28","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1109\/LCOMM.2015.2506576","volume":"20","author":"Y Qi","year":"2016","unstructured":"Qi, Y., Tang, C., Huang, D.: Binary linear codes with few weights. IEEE Commun. Lett. 20(2), 208\u2013211 (2016)","journal-title":"IEEE Commun. Lett."},{"issue":"3","key":"361_CR29","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1007\/s10623-016-0267-7","volume":"83","author":"C Tang","year":"2017","unstructured":"Tang, C., Xiang, C., Feng, K.: Linear codes with few weights from inhomogeneous quadratic functions. Des. Codes Cryptogr. 83(3), 691\u2013714 (2017)","journal-title":"Des. Codes Cryptogr."},{"issue":"7","key":"361_CR30","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1109\/LCOMM.2015.2431253","volume":"19","author":"Q Wang","year":"2015","unstructured":"Wang, Q., Ding, K., Xue, R.: Binary linear codes with two weights. IEEE Commun. Lett. 19(7), 1097\u20131100 (2015)","journal-title":"IEEE Commun. Lett."},{"issue":"3","key":"361_CR31","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s12095-015-0180-3","volume":"9","author":"Q Wang","year":"2017","unstructured":"Wang, Q., Ding, K., Lin, D., Xue, R.: A kind of three-weight linear codes. Cryptogr. Commun. 9(3), 315\u2013322 (2017)","journal-title":"Cryptogr. Commun."},{"key":"361_CR32","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.ffa.2017.08.001","volume":"48","author":"S Yang","year":"2017","unstructured":"Yang, S., Kong, X., Tang, C.: A construction of linear codes and their complete weight enumerators. Finite Fields Their Appl. 48, 196\u2013226 (2017)","journal-title":"Finite Fields Their Appl."},{"key":"361_CR33","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s12095-016-0187-4","volume":"9","author":"S Yang","year":"2017","unstructured":"Yang, S., Yao, Z.-A., Zhao, C.-A.: A class of three-weight linear codes and their complete weight enumerators. Cryptogr. Commun. 9, 133\u2013149 (2017)","journal-title":"Cryptogr. Commun."},{"issue":"3","key":"361_CR34","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1007\/s10623-016-0191-x","volume":"82","author":"S Yang","year":"2017","unstructured":"Yang, S., Yao, Z.-A.: Complete weight enumerators of a family of three-weight linear codes. Des. Codes Cryptogr. 82(3), 663\u2013674 (2017)","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"361_CR35","doi-asserted-by":"publisher","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":"361_CR36","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1109\/TIT.2005.860412","volume":"52","author":"J Yuan","year":"2006","unstructured":"Yuan, J., Ding, C.: Secret sharing schemes from three classes of linear codes. IEEE Trans. Inf. Theory 52(1), 206\u2013212 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"361_CR37","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s12095-016-0190-9","volume":"9","author":"D Zhang","year":"2017","unstructured":"Zhang, D., Fan, C., Peng, D., Tang, X.: Complete weight enumerators of some linear codes from quadratic forms. Cryptogr. Commun. 9, 151\u2013163 (2017)","journal-title":"Cryptogr. Commun."},{"key":"361_CR38","doi-asserted-by":"publisher","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 Their Appl. 25, 79\u201393 (2014)","journal-title":"Finite Fields Their Appl."},{"issue":"2","key":"361_CR39","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s10623-015-0144-9","volume":"81","author":"Z Zhou","year":"2016","unstructured":"Zhou, Z., Li, N., Fan, C., Helleseth, T.: Linear codes with two or three weights from quadratic bent functions. Des. Codes Cryptogr. 81(2), 283\u2013295 (2016)","journal-title":"Des. Codes Cryptogr."}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00200-018-0361-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-018-0361-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-018-0361-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T00:35:51Z","timestamp":1559090151000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00200-018-0361-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,29]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["361"],"URL":"https:\/\/doi.org\/10.1007\/s00200-018-0361-3","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,29]]},"assertion":[{"value":"30 July 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 May 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}