{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T19:37:40Z","timestamp":1777750660828,"version":"3.51.4"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s00200-023-00637-z","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T23:02:24Z","timestamp":1703718144000},"page":"783-802","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A class of BCH codes with length $$\\frac{q^{2m}-1}{q+1}$$"],"prefix":"10.1007","volume":"36","author":[{"given":"Binbin","family":"Pang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoshan","family":"Kai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,27]]},"reference":[{"key":"637_CR1","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1109\/TIT.2006.890730","volume":"53","author":"SA Aly","year":"2007","unstructured":"Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inform. Theory 53, 1183\u20131188 (2007)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1","key":"637_CR2","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/S0019-9958(60)90287-4","volume":"3","author":"R Bose","year":"1960","unstructured":"Bose, R., Ray-Chaudhuri, D.: On a class of error correcting binary group codes. Inf. Control 3(1), 68\u201379 (1960)","journal-title":"Inf. Control"},{"key":"637_CR3","first-page":"963","volume-title":"Handbook Coding Theory","author":"P Charpin","year":"1998","unstructured":"Charpin, P.: Open problems on cyclic codes. In: Pless, V.S., Huffman, W.C. (eds.) Handbook Coding Theory, vol. 1, pp. 963\u20131063. Elsevier, Amsterdam (1998)"},{"issue":"1","key":"637_CR4","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1109\/18.50397","volume":"36","author":"P Charpin","year":"1990","unstructured":"Charpin, P.: On a class of primitive BCH codes. IEEE Trans. Inf. Theory 36(1), 222\u2013228 (1990)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"637_CR5","doi-asserted-by":"publisher","first-page":"1727","DOI":"10.1109\/TIT.2006.871605","volume":"52","author":"P Charpin","year":"2006","unstructured":"Charpin, P., Helleseth, T., Zinoviev, V.A.: The coset distribution of triple-error-correcting binary primitive BCH codes. IEEE Trans. Inf. Theory 52(4), 1727\u20131732 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"637_CR6","doi-asserted-by":"publisher","first-page":"2351","DOI":"10.1109\/TIT.2015.2409838","volume":"61","author":"C Ding","year":"2015","unstructured":"Ding, C., Du, X., Zhou, Z.: The Bose and minimum distance of a class of BCH codes. IEEE Trans. Inf. Theory 61(5), 2351\u20132356 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"637_CR7","doi-asserted-by":"publisher","first-page":"5322","DOI":"10.1109\/TIT.2015.2470251","volume":"61","author":"C Ding","year":"2015","unstructured":"Ding, C.: Parameters of several classes of BCH codes. IEEE Trans. Inf. Theory 61(10), 5322\u20135330 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"637_CR8","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/j.ffa.2016.12.009","volume":"45","author":"C Ding","year":"2017","unstructured":"Ding, C., Fan, C., Zhou, Z.: The dimension and minimum distance of two classes of primitive BCH codes. Finite Fields Appl. 45, 237\u2013263 (2017)","journal-title":"Finite Fields Appl."},{"issue":"11","key":"637_CR9","doi-asserted-by":"publisher","first-page":"6774","DOI":"10.1109\/TIT.2020.2991635","volume":"66","author":"Z Du","year":"2020","unstructured":"Du, Z., Li, C., Mesnager, S.: Constructions of self-orthogonal codes from Hulls of BCH codes and their parameters. IEEE Trans. Inf. Theory 66(11), 6774\u20136785 (2020)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"637_CR10","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1109\/TIT.1986.1057215","volume":"32","author":"T Fujiwara","year":"1986","unstructured":"Fujiwara, T., Takata, T., Kasami, T., Lin, S.: An approximation to the weight distribution of binary primitive BCH codes with designed distances 9 and 11(Corresp.). IEEE Trans. Inf. Theory 32(5), 706\u2013709 (1986)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"637_CR11","doi-asserted-by":"publisher","first-page":"1070","DOI":"10.1109\/LCOMM.2020.3043448","volume":"25","author":"C Gan","year":"2021","unstructured":"Gan, C., Li, C., Qian, H.: Parameters of Hulls of primitive BCH codes of length $$q^3-1$$. IEEE Commun. Lett. 25(4), 1070\u20131073 (2021)","journal-title":"IEEE Commun. Lett."},{"issue":"10","key":"637_CR12","doi-asserted-by":"publisher","first-page":"6442","DOI":"10.1109\/TIT.2021.3076878","volume":"67","author":"C Gan","year":"2021","unstructured":"Gan, C., Li, C., Mesnager, S., Qian, H.: On hulls of some primitive BCH codes and self-orthogonal codes. IEEE Trans. Inf. Theory 67(10), 6442\u20136455 (2021)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"637_CR13","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1109\/TIT.2021.3125933","volume":"68","author":"B Gong","year":"2022","unstructured":"Gong, B., Ding, C., Li, C.: The dual codes of several classes of BCH codes. IEEE Trans. Inform. Theory 68(2), 953\u2013964 (2022)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"637_CR14","first-page":"147","volume":"2","author":"A Hocquenghem","year":"1959","unstructured":"Hocquenghem, A.: Codes correcteurs d\u2019erreurs. Chiffres (Paris) 2, 147\u2013156 (1959)","journal-title":"Chiffres (Paris)"},{"issue":"6","key":"637_CR15","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1109\/TIT.1972.1054903","volume":"18","author":"T Kasami","year":"1972","unstructured":"Kasami, T., Lin, S.: Some results on the minimum weight of primitive BCH codes. IEEE Trans. Inf. Theory 18(6), 824\u2013825 (1972)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"637_CR16","unstructured":"Kasami, T.: Weight distributions of Bose\u2013Chaudhuri\u2013Hocquenghem codes. In: R.C. Bose, T.A. Dowlings (Eds.), Combinatorial Mathematics and Applications, Univ. North Carolina Press, Chapel Hill, NC, Ch.20 (1969)"},{"key":"637_CR17","doi-asserted-by":"publisher","first-page":"3830","DOI":"10.1109\/TIT.2018.2883615","volume":"65","author":"C Li","year":"2019","unstructured":"Li, C., Wu, P., Liu, F.: On two classes of primitive BCH codes and some related codes. IEEE Trans. Inf. Theory 65, 3830\u20133840 (2019)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"637_CR18","doi-asserted-by":"publisher","first-page":"2530","DOI":"10.1137\/16M1108431","volume":"31","author":"S Li","year":"2017","unstructured":"Li, S.: The minimum distance of some narrow-sense primitive BCH codes. SIAM J. Discrete Math. 31, 2530\u20132569 (2017)","journal-title":"SIAM J. Discrete Math."},{"issue":"9","key":"637_CR19","first-page":"5699","volume":"63","author":"S Li","year":"2017","unstructured":"Li, S., Li, C., Ding, C., Liu, H.: Two families of LCD BCH codes. IEEE Trans. Inf. Theory 63(9), 5699\u20135717 (2017)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"637_CR20","doi-asserted-by":"publisher","first-page":"4344","DOI":"10.1109\/TIT.2017.2672961","volume":"63","author":"C Li","year":"2017","unstructured":"Li, C., Ding, C., Li, S.: LCD cyclic codes over finite fields. IEEE Trans. Inform. Theory 63, 4344\u20134356 (2017)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"637_CR21","doi-asserted-by":"publisher","first-page":"1910","DOI":"10.1016\/j.disc.2017.04.001","volume":"340","author":"H Liu","year":"2017","unstructured":"Liu, H., Ding, C., Li, C.: Dimensions of three types of BCH codes over $$GF(q)$$. Discret. Math. 340, 1910\u20131927 (2017)","journal-title":"Discret. Math."},{"key":"637_CR22","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.ffa.2018.09.005","volume":"55","author":"Y Liu","year":"2019","unstructured":"Liu, Y., Li, R., Fu, Q., Lu, L., Rao, Y.: Some binary BCH codes with length $$n=2^m+1$$. Finite Fields Appl. 55, 109\u2013133 (2019)","journal-title":"Finite Fields Appl."},{"issue":"11","key":"637_CR23","doi-asserted-by":"publisher","first-page":"7219","DOI":"10.1109\/TIT.2017.2743687","volume":"63","author":"S Li","year":"2017","unstructured":"Li, S., Ding, C., Xiong, M., Ge, G.: Narrow-Sense BCH codes over GF$$(q)$$ with length $$n=\\frac{q^m-1}{q-1}$$. IEEE Trans. Inf. Theory 63(11), 7219\u20137236 (2017)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"637_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2019.101581","volume":"60","author":"P Wu","year":"2019","unstructured":"Wu, P., Li, C., Peng, W.: On some cyclic codes of length $$n=\\frac{q^{2m}-1}{q+1}$$. Finite Fields Appl. 60, 101581 (2019)","journal-title":"Finite Fields Appl."},{"key":"637_CR25","doi-asserted-by":"publisher","first-page":"579","DOI":"10.3934\/amc.2018034","volume":"12","author":"H Yan","year":"2018","unstructured":"Yan, H., Liu, H., Li, C., Yang, S.: Parameters of LCD BCH codes with two lengths. Adv. Math. Commun. 12, 579\u2013594 (2018)","journal-title":"Adv. Math. Commun."},{"key":"637_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00200-017-0320-4","volume":"29","author":"H Yan","year":"2018","unstructured":"Yan, H.: A class of primitive BCH codes and their weight distribution. AAECC 29, 1\u201311 (2018)","journal-title":"AAECC"},{"key":"637_CR27","first-page":"216","volume":"13","author":"D Yue","year":"1996","unstructured":"Yue, D., Hu, Z.: On the dimension and minimum distance of BCH codes over GF$$(q)$$. J. Electronics 13, 216\u2013221 (1996)","journal-title":"J. Electronics"},{"key":"637_CR28","doi-asserted-by":"publisher","first-page":"2625","DOI":"10.1109\/18.887870","volume":"46","author":"D Yue","year":"2000","unstructured":"Yue, D., Feng, G.: Minimum cyclotomic coset representatives and their applications to BCH codes and Goppa codes. IEEE Trans. Inform. Theory 46, 2625\u20132628 (2000)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"637_CR29","doi-asserted-by":"publisher","first-page":"2139","DOI":"10.1007\/s10623-017-0441-6","volume":"86","author":"S Zhu","year":"2018","unstructured":"Zhu, S., Sun, Z., Li, P.: A class of negacyclic BCH codes and its application to quantum codes. Des. Codes Cryptogr. 86, 2139\u20132165 (2018)","journal-title":"Des. Codes Cryptogr."},{"issue":"3","key":"637_CR30","doi-asserted-by":"publisher","first-page":"1683","DOI":"10.1109\/TIT.2021.3131810","volume":"68","author":"H Zhu","year":"2022","unstructured":"Zhu, H., Shi, M., Wang, X., Helleseth, T.: The $$q$$-ary antiprimitive BCH codes. IEEE Trans. Inf. Theory 68(3), 1683\u20131695 (2022)","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-023-00637-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-023-00637-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-023-00637-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T12:24:27Z","timestamp":1749471867000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-023-00637-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,27]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["637"],"URL":"https:\/\/doi.org\/10.1007\/s00200-023-00637-z","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,27]]},"assertion":[{"value":"25 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 May 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}