{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T17:45:26Z","timestamp":1767980726882,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T00:00:00Z","timestamp":1649635200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T00:00:00Z","timestamp":1649635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P1-0404"],"award-info":[{"award-number":["P1-0404"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["J1-9108"],"award-info":[{"award-number":["J1-9108"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["J1-1694"],"award-info":[{"award-number":["J1-1694"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972400"],"award-info":[{"award-number":["61972400"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61872103"],"award-info":[{"award-number":["61872103"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Guangxi Natural Science Foundation","doi-asserted-by":"crossref","award":["2019GXNSFGA245004"],"award-info":[{"award-number":["2019GXNSFGA245004"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Guangxi Science and Technology Foundation","award":["Guike AB18281019"],"award-info":[{"award-number":["Guike AB18281019"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2022,5]]},"DOI":"10.1007\/s10623-022-01037-z","type":"journal-article","created":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T14:02:51Z","timestamp":1649685771000},"page":"1289-1318","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Minimal binary linear codes: a general framework based on bent concatenation"],"prefix":"10.1007","volume":"90","author":[{"given":"Fengrong","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Enes","family":"Pasalic","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2894-3871","authenticated-orcid":false,"given":"Ren\u00e9","family":"Rodr\u00edguez","sequence":"additional","affiliation":[]},{"given":"Yongzhuang","family":"Wei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"1037_CR1","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2020104","author":"GN Alfarano","year":"2020","unstructured":"Alfarano G.N., Borello M., Neri A.: A geometric characterization of minimal codes and their asymptotic performance. Adv. Math. Commun. (2020). https:\/\/doi.org\/10.3934\/amc.2020104.","journal-title":"Adv. Math. Commun."},{"issue":"5","key":"1037_CR2","doi-asserted-by":"publisher","first-page":"2010","DOI":"10.1109\/18.705584","volume":"44","author":"A Ashikhmin","year":"1998","unstructured":"Ashikhmin A., Barg A.: Minimal vectors in linear codes. IEEE Trans. Inf. Theory 44(5), 2010\u20132017 (1998).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"1037_CR3","doi-asserted-by":"publisher","first-page":"4152","DOI":"10.1109\/TIT.2019.2891992","volume":"65","author":"D Bartoli","year":"2019","unstructured":"Bartoli D., Bonini M.: Minimal linear codes in odd characteristic. IEEE Trans. Inf. Theory 65(7), 4152\u20134155 (2019).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1037_CR4","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s10623-016-0229-0","volume":"82","author":"S Bhattacharya","year":"2017","unstructured":"Bhattacharya S., Sarkar S.: On some permutation binomials and trinomials over $${\\mathbb{F}}_{2^{n}}$$. Des. Codes Cryptogr. 82, 149\u2013160 (2017).","journal-title":"Des. Codes Cryptogr."},{"key":"1037_CR5","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10801-019-00930-6","volume":"53","author":"M Bonini","year":"2021","unstructured":"Bonini M., Borello M.: Minimal linear codes arising from blocking sets. J. Algebr. Comb. 53, 327\u2013341 (2021).","journal-title":"J. Algebr. Comb."},{"key":"1037_CR6","volume-title":"Boolean Functions for Cryptography and Coding Theory","author":"C Carlet","year":"2021","unstructured":"Carlet C.: Boolean Functions for Cryptography and Coding Theory. Cambridge University Press, Cambridge (2021)."},{"key":"1037_CR7","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1008344232130","volume":"15","author":"C Carlet","year":"1998","unstructured":"Carlet C., Charpin P., Zinoviev V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. Des. Codes Cryptogr. 15, 125\u2013156 (1998).","journal-title":"Des. Codes Cryptogr."},{"issue":"6","key":"1037_CR8","doi-asserted-by":"publisher","first-page":"2089","DOI":"10.1109\/TIT.2005.847722","volume":"51","author":"C Carlet","year":"2005","unstructured":"Carlet C., Ding C., Yuan J.: Linear codes from highly nonlinear functions and their secret sharing schemes. IEEE Trans. Inf. Theory 51(6), 2089\u20132102 (2005).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1037_CR9","doi-asserted-by":"publisher","first-page":"2167","DOI":"10.1007\/s10623-017-0442-5","volume":"86","author":"S Chang","year":"2018","unstructured":"Chang S., Hyun J.: Linear codes from simplicial complexes. Des. Codes Cryptogr. 86, 2167\u20132181 (2018).","journal-title":"Des. Codes Cryptogr."},{"key":"1037_CR10","doi-asserted-by":"crossref","unstructured":"Cohen G., Mesnager S., Patey A.: On minimal and quasi-minimal linear codes. In: Stam, M. (eds.) Proc. IMACC (Lect. Notes Comput. Sci., vol. 8308), pp. 85\u201398. Springer-Verlag, Berlin (2013)","DOI":"10.1007\/978-3-642-45239-0_6"},{"issue":"6","key":"1037_CR11","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"},{"key":"1037_CR12","doi-asserted-by":"crossref","unstructured":"Ding C.: A construction of binary linear codes from Boolean functions. discret. Math. 339(9), 2288\u20132303 (2016).","DOI":"10.1016\/j.disc.2016.03.029"},{"key":"1037_CR13","doi-asserted-by":"crossref","unstructured":"Ding C., Yuan, J.: Covering and secret sharing with linear codes. In: Calude, C., Dinneen M., Vajnovszki V. (eds) discret. Math. Theor. Comput. Sci. (Lect. Notes Comput. Sci., vol. 2731), pp. 11\u201325. Springer, Berlin, Heidelberg (2003)","DOI":"10.1007\/3-540-45066-1_2"},{"issue":"10","key":"1037_CR14","doi-asserted-by":"publisher","first-page":"6536","DOI":"10.1109\/TIT.2018.2819196","volume":"64","author":"C Ding","year":"2018","unstructured":"Ding C., Heng Z., Zhou Z.: Minimal binary linear codes. IEEE Trans. Inf. Theory 64(10), 6536\u20136545 (2018).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1037_CR15","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1016\/j.ffa.2018.08.010","volume":"54","author":"Z Heng","year":"2018","unstructured":"Heng Z., Ding C., Zhou Z.: Minimal linear codes over finite fields. Finite Fields Appl. 54, 176\u2013196 (2018).","journal-title":"Finite Fields Appl."},{"issue":"9","key":"1037_CR16","doi-asserted-by":"publisher","first-page":"5387","DOI":"10.1109\/TIT.2020.2970405","volume":"66","author":"Z Heng","year":"2020","unstructured":"Heng Z., Ding C., Wang W.: Optimal binary linear codes from maximal arcs. IEEE Trans. Inf. Theory 66(9), 5387\u20135394 (2020).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1037_CR17","doi-asserted-by":"crossref","unstructured":"Jaffe D.: Optimal binary linear codes of length $$\\le 30$$. discret. Math. 223(1), 135\u2013155 (2000).","DOI":"10.1016\/S0012-365X(99)00135-1"},{"key":"1037_CR18","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s10623-019-00682-1","volume":"88","author":"X Li","year":"2020","unstructured":"Li X., Yue Q.: Four classes of minimal binary linear codes with $$w_{min}\/w_{max} <1\/2$$ derived from Boolean functions. Des. Codes Cryptogr. 88, 257\u2013271 (2020).","journal-title":"Des. Codes Cryptogr."},{"key":"1037_CR19","volume-title":"The Theory of Error-Correcting Codes","author":"F MacWilliams","year":"1977","unstructured":"MacWilliams F., Sloane N.: The Theory of Error-Correcting Codes. North Holland, Amsterdam (1977)."},{"key":"1037_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0097-3165(73)90031-9","volume":"15","author":"R McFarland","year":"1973","unstructured":"McFarland R.: A family of difference sets in non-cyclic groups. J. Comb. Theory (series A) 15, 1\u201310 (1973).","journal-title":"J. Comb. Theory (series A)"},{"key":"1037_CR21","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s12095-016-0186-5","volume":"9","author":"S Mesnager","year":"2017","unstructured":"Mesnager S.: Linear codes with few weights from weakly regular bent functions based on a generic construction. Cryptogr. Commun. 9, 71\u201384 (2017).","journal-title":"Cryptogr. Commun."},{"key":"1037_CR22","first-page":"463","volume-title":"Concise Encycl. Coding Theory","author":"S Mesnager","year":"2021","unstructured":"Mesnager S.: Linear codes from functions. In: Huffman W.C., Kim J., Sol\u00e9 P. (eds.) Concise Encycl. Coding Theory, pp. 463\u2013526. Chapman and Hall\/CRC, London (2021)."},{"issue":"4","key":"1037_CR23","doi-asserted-by":"publisher","first-page":"2296","DOI":"10.1109\/TIT.2019.2956130","volume":"66","author":"S Mesnager","year":"2020","unstructured":"Mesnager S., S\u0131nak A.: Several classes of minimal linear codes with few weights from weakly regular plateaued functions. IEEE Trans. Inf. Theory 66(4), 2296\u20132310 (2020).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2\u20133","key":"1037_CR24","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s10623-018-0556-4","volume":"87","author":"S Mesnager","year":"2019","unstructured":"Mesnager S., \u00d6zbudak F., S\u0131nak A.: Linear codes from weakly regular plateaued functions and their secret sharing schemes. Des. Codes Cryptogr. 87(2\u20133), 463\u2013480 (2019).","journal-title":"Des. Codes Cryptogr."},{"issue":"4","key":"1037_CR25","first-page":"77","volume":"8","author":"S Mesnager","year":"2019","unstructured":"Mesnager S., S\u0131nak A., Yayla O.: Minimal linear codes with few weights and their secret sharing. Int. J. Inf. Secur. Sci. 8(4), 77\u201387 (2019).","journal-title":"Int. J. Inf. Secur. Sci."},{"issue":"9","key":"1037_CR26","doi-asserted-by":"publisher","first-page":"5404","DOI":"10.1109\/TIT.2020.2978387","volume":"66","author":"S Mesnager","year":"2020","unstructured":"Mesnager S., Qi Y., Ru H., Tang C.: Minimal linear codes from characteristic functions. IEEE Trans. Inf. Theory 66(9), 5404\u20135413 (2020).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1037_CR27","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1007\/s12095-021-00491-1","volume":"13","author":"E Pasalic","year":"2021","unstructured":"Pasalic E., Rodr\u00edguez R., Zhang F., Wei Y.: Several classes of minimal binary linear codes violating the Aschikhmin\u2013Barg bound. Cryptogr. Commun. 13, 637\u2013659 (2021).","journal-title":"Cryptogr. Commun."},{"key":"1037_CR28","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/0097-3165(76)90024-8","volume":"20","author":"O Rothaus","year":"1976","unstructured":"Rothaus O.: On bent functions. J. Comb. Theory (series A) 20, 300\u2013305 (1976).","journal-title":"J. Comb. Theory (series A)"},{"key":"1037_CR29","doi-asserted-by":"crossref","unstructured":"S\u0131nak A.: Minimal linear codes from weakly regular plateaued balanced functions. discret. Math. 344(3), 112215 (2021).","DOI":"10.1016\/j.disc.2020.112215"},{"key":"1037_CR30","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1007\/s12095-019-00412-3","volume":"12","author":"D Tang","year":"2020","unstructured":"Tang D., Li X.: A note on the minimal binary linear code. Cryptogr. Commun. 12, 375\u2013388 (2020).","journal-title":"Cryptogr. Commun."},{"key":"1037_CR31","doi-asserted-by":"crossref","unstructured":"Tang D., Carlet C., Zhou Z.: Binary linear codes from vectorial Boolean functions and their weight distribution. discret. Math. 340(12), 3055\u20133072 (2017).","DOI":"10.1016\/j.disc.2017.07.008"},{"issue":"6","key":"1037_CR32","doi-asserted-by":"publisher","first-page":"3690","DOI":"10.1109\/TIT.2021.3070377","volume":"67","author":"C Tang","year":"2021","unstructured":"Tang C., Qiu Y., Liao Q., Zhou Z.: Full characterization of minimal linear codes as cutting blocking sets. IEEE Trans. Inf. Theory 67(6), 3690\u20133700 (2021).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1037_CR33","doi-asserted-by":"crossref","unstructured":"Wolfmann J.: The weights of the orthogonal of certain cyclic codes or extended Goppa codes. In: Mora T. (eds) Appl. Algebra Algebr. Algorithms Error-Correcting Codes. AAECC 1988 (Lect. Notes Comput. Sci., vol 357), pp. 476\u2013480. Springer, Berlin (1989)","DOI":"10.1007\/3-540-51083-4_84"},{"issue":"11","key":"1037_CR34","doi-asserted-by":"publisher","first-page":"7067","DOI":"10.1109\/TIT.2019.2918537","volume":"65","author":"G Xu","year":"2019","unstructured":"Xu G., Qu L.: Three classes of minimal linear codes over the finite fields of odd characteristic. IEEE Trans. Inf. Theory 65(11), 7067\u20137078 (2019).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1037_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2020.101688","author":"G Xu","year":"2020","unstructured":"Xu G., Qu L., Cao X.: Minimal linear codes from Maiorana\u2013McFarland functions. Finite Fields Appl. (2020). https:\/\/doi.org\/10.1016\/j.ffa.2020.101688.","journal-title":"Finite Fields Appl."},{"key":"1037_CR36","unstructured":"Xu G., Qu L., Luo G.: Minimal linear codes from weakly regular bent functions. The 11th Int. Conf. Seq. Appl. (SETA 2020), September 22\u201325, Saint Petersburg, Russia (2020)"},{"issue":"1","key":"1037_CR37","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":"1037_CR38","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s00200-018-0367-x","volume":"30","author":"W Zhang","year":"2019","unstructured":"Zhang W., Yan H., Wei H.: Four families of minimal binary linear codes with $$w_{min}\/w_{max}\\le 1\/2$$. Appl. Algebra Eng. Commun. Comput. 30, 75\u2013184 (2019).","journal-title":"Appl. Algebra Eng. Commun. Comput."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01037-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-022-01037-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-022-01037-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,25]],"date-time":"2022-04-25T19:10:26Z","timestamp":1650913826000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-022-01037-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,11]]},"references-count":38,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,5]]}},"alternative-id":["1037"],"URL":"https:\/\/doi.org\/10.1007\/s10623-022-01037-z","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,11]]},"assertion":[{"value":"20 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}