{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T17:36:03Z","timestamp":1776965763858,"version":"3.51.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"University of Kocaeli"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>A multisecret-sharing scheme is a method for distributing <jats:bold>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:bold> randomly associated secrets <jats:bold>\n              <jats:italic>s<\/jats:italic>\n            <\/jats:bold>\n            <jats:sub>1<\/jats:sub>, <jats:bold>\n              <jats:italic>s<\/jats:italic>\n            <\/jats:bold>\n            <jats:sub>2<\/jats:sub>,..., <jats:bold>\n              <jats:italic>s<\/jats:italic>\n            <\/jats:bold>\n            <jats:sub>n<\/jats:sub> among a set of attendants. Linear codes with complementary duals, LCD codes, form an important class of linear codes, while weighing orthogonal matrices play a significant role in cryptography. In this paper, we design novel multisecret-sharing schemes based on LCD codes derived from weighing orthogonal matrices. We analyze the access structures, coalition statistics, security aspects, and information-theoretic efficiency compared to existing multisecret-sharing methods.<\/jats:p>","DOI":"10.1007\/s12190-025-02493-1","type":"journal-article","created":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T11:15:33Z","timestamp":1744974933000},"page":"6181-6205","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Enhanced multisecret-sharing schemes using LCD codes and weighing orthogonal matrices"],"prefix":"10.1007","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1502-123X","authenticated-orcid":false,"given":"Selda","family":"\u00c7alkavur","sequence":"first","affiliation":[]},{"given":"Patrick","family":"Sol\u00e9","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,18]]},"reference":[{"issue":"4","key":"2493_CR1","doi-asserted-by":"publisher","first-page":"3010","DOI":"10.1109\/TIT.2018.2789347","volume":"64","author":"C Carlet","year":"2018","unstructured":"Carlet, C., Sihem Mesnager, C.T., Qi, Y., Pellikaan, R.: Linear codes over Fq are equivalent to LCD codes for q > 3. IEEE Trans. Inf. Theor. 64(4), 3010\u20133017 (2018)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"5","key":"2493_CR2","doi-asserted-by":"publisher","first-page":"816","DOI":"10.4153\/CJM-1971-091-x","volume":"23","author":"P Delsarte","year":"1971","unstructured":"Delsarte, P., Goethals, J.M., Seidel, J.J.: Orthogonal matrices with zero diagonal-II. Can. J. Math. 23(5), 816\u2013832 (1971)","journal-title":"Canadian Journal of Mathematics"},{"key":"2493_CR3","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/B978-0-12-189420-7.50024-4","volume-title":"Geometrics and Combinatorics","author":"JM Goethals","year":"1991","unstructured":"Goethals, J.M., Seidel, JJ.: Orthogonal matrices with zero diagonal. In: Geometrics and Combinatorics, pp. 257\u2013266. Elsevier (1991)"},{"issue":"13","key":"2493_CR4","doi-asserted-by":"publisher","first-page":"623","DOI":"10.12988\/ams.2019.9682","volume":"13","author":"N Matsuki","year":"2019","unstructured":"Matsuki, N.: A construction of special orthogonal matrices. Appl. Math. Sci. 13(13), 623\u2013625 (2019)","journal-title":"Applied Mathematical Sciences"},{"key":"2493_CR5","doi-asserted-by":"publisher","first-page":"120381","DOI":"10.1109\/ACCESS.2021.3107579","volume":"9","author":"K-H Chan","year":"2021","unstructured":"Chan, K-H., Ke, W., Im, S-K.: A general method for generating discrete orthogonal matrices. IEEE Access. 9, 120381\u2013120391 (2021)","journal-title":"IEEE Access"},{"key":"2493_CR6","doi-asserted-by":"crossref","unstructured":"Dougherty, S.K., Kim, J-L., Ozkaya, B., Sok, L., Sol\u00e9 P.: The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices. Int. J. Inf. Coding Theor. 4, (2\/3), 116\u2013128 (2017)","DOI":"10.1504\/IJICOT.2017.083827"},{"key":"2493_CR7","doi-asserted-by":"crossref","unstructured":"Ephremidze, L., Spitkovsky, I.: Random generator of orthogonal matrices in finite fields. In: Arai, K., (ed.) Advances in Information and Communication. FICC 2024. Lecture Notes in Networks and Systems, vol 920, Springer, Cham","DOI":"10.1007\/978-3-031-53963-3_20"},{"key":"2493_CR8","doi-asserted-by":"crossref","unstructured":"Hill, L.S., In Algebraic Alphabet C.: The American Mathematical Monthly, June-July. 36(6), 306\u2013312 (1929)","DOI":"10.1080\/00029890.1929.11986963"},{"key":"2493_CR9","doi-asserted-by":"crossref","unstructured":"Kumari, S., Mahato, H.: Construction of weighted orthogonal matrices over finite field and its application in cryptography. Int. J. Inf. Comp. Secur. 22(3\/4) (2023)","DOI":"10.1504\/IJICS.2023.135894"},{"issue":"4","key":"2493_CR10","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1080\/10586458.2005.10128935","volume":"14","author":"R Harkins","year":"2005","unstructured":"Harkins, R., Weber, E., Westmeyer, A.: Encryption schemes using finite frames and Hadamard arrays. Exp. Math. 14(4), 423\u2013432 (2005)","journal-title":"Experimental Mathematics"},{"key":"2493_CR11","unstructured":"Kamyun, N., Pingyot, K.: Encryption schemes using anti-orthogonal of type I matrices. Thai J. Math. 19(4), 1671\u20131683"},{"key":"2493_CR12","doi-asserted-by":"crossref","unstructured":"Blakley, G.R.: Safeguarding cryptographic keys, In Proceedings of the 1979 National Computer Conference, New York, NY, USA, 4\u20137 June 1979, pp. 313\u2013317.","DOI":"10.1109\/MARK.1979.8817296"},{"issue":"1","key":"2493_CR13","first-page":"17","volume":"3","author":"C Koukouvinos","year":"2013","unstructured":"Koukouvinos, C., Simas, DE.: Encryption schemes based on Hadamard matrices with circulant cores. J. Appl. Math. Bioinformatics. 3(1), 17\u201341 (2013)","journal-title":"Journal of Applied Mathematics and Bioinformatics"},{"key":"2493_CR14","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1145\/359168.359176","volume":"22","author":"A Shamir","year":"1979","unstructured":"Shamir A: How to share a secret, Commun. ACM. 22, 612\u2013613 (1979)","journal-title":"ACM"},{"key":"2493_CR15","doi-asserted-by":"crossref","unstructured":"Dougherty, S.T., Mesnager, S., Sol\u00e9. P.: Secret sharing schemes based on self-dual codes, In 2008, IEEE Information theory workshop, pp. 338\u2013342, 2008.","DOI":"10.1109\/ITW.2008.4578681"},{"key":"2493_CR16","volume-title":"International journal of security and networks","author":"L Bai","year":"2009","unstructured":"Bai, L., Zou, X.: A proactive secret sharing scheme in matrix projection method. Int. J. Secur. Netw. 4, In Press (2009)"},{"key":"2493_CR17","first-page":"1023","volume":"3","author":"A Das","year":"1997","unstructured":"Das, A., Adhikari, A.: An efficient multi-use multi-secret sharing schemes and error correcting codes. J. Comput. Sci. 3, 1023\u20131036 (1997)","journal-title":"J. Comput. Sci"},{"issue":"5","key":"2493_CR18","doi-asserted-by":"publisher","first-page":"584","DOI":"10.1002\/sec.576","volume":"6","author":"CS Chum","year":"2013","unstructured":"Chum, C.S., Zhang, X.: Hash function-based secret sharing scheme designs. Secur Commun. Netw. 6(5), 584\u2013592 (2013)","journal-title":"Security and communication networks"},{"issue":"1","key":"2493_CR19","first-page":"2","volume":"14","author":"H Pilaram","year":"2017","unstructured":"Pilaram, H., Eghlidos, T.: An efficient lattice based multi-stage secret sharing scheme. IEEE Trans. Depend. Secure Comput. 14(1), 2\u20138 (2017)","journal-title":"IEEE Transactions on Dependable and Secure Computing"},{"key":"2493_CR20","doi-asserted-by":"crossref","unstructured":"Ding, J., Lin, C., Mesnager, S.: Secret sharing schemes based on the dual of Golay codes, Cryptogr. Commun. 13, 1023\u20131041","DOI":"10.1007\/s12095-021-00531-w"},{"key":"2493_CR21","first-page":"1023","volume":"3","author":"C Ding","year":"1997","unstructured":"Ding, C., Laihonen, T., Renvall, A.: Linear multisecret-sharing schemes and error correcting codes. J. Comput. Sci. 3, 1023\u20131036 (1997)","journal-title":"J. Comput. Sci"},{"key":"2493_CR22","doi-asserted-by":"publisher","DOI":"10.1142\/12585","volume-title":"Code Based Secret Sharing Schemes","author":"S \u00c7alkavur","year":"2022","unstructured":"\u00c7alkavur, S., Bonnecaze, A., Cruz, R.D., Sol\u00e9, P.: Code Based Secret Sharing Schemes. World Scientific Publishing, Singapore (2022)"},{"key":"2493_CR23","doi-asserted-by":"crossref","unstructured":"Li, L., Li, Z.: An efficient quantum secret sharing scheme based on restricted threshold access structure, Entropy (Basel), 25(2), 263 (2023)","DOI":"10.3390\/e25020265"},{"issue":"e262","key":"2493_CR24","first-page":"1","volume":"5","author":"S Saurabh","year":"2022","unstructured":"Saurabh, S., Sinha, K.: Perfect secret sharing schemes from combinatorial squares. Secur Privacy. 5(e262), 1\u20139 (2022)","journal-title":"Security and Privacy"},{"key":"2493_CR25","doi-asserted-by":"crossref","unstructured":"Melakhessou, A., Chatouh, K., Guenda, K.: DNA multi-secret sharing schemes based on linear codes over Z4 x R. J. Appl. Math. Comput. 6, 23 (06\u201312\u20132023)","DOI":"10.1007\/s12190-023-01941-0"},{"key":"2493_CR26","unstructured":"Rathi, D., Kumar, S.: Quantum multi-secret sharing scheme with access structures and cheat identification. preprint submitted to Elsevier, arXiv: 2309.06458v2 [quant-ph. 20 Oct. 2023"},{"key":"2493_CR27","volume-title":"Erasure techniques in MRD codes","author":"WB Vasantha","year":"2012","unstructured":"Vasantha, W.B., et al.: Erasure techniques in MRD codes. Zip Publishing, Ohio (2012)"},{"key":"2493_CR28","first-page":"107","volume":"94","author":"S \u00c7alkavur","year":"2017","unstructured":"\u00c7alkavur, S., Sol\u00e9, P.: Multisecret sharing schemes and bounded distance decoding of linear codes. Int. J. Comput. 94, 107\u2013114 (2017)","journal-title":"Int. J. Comput"},{"key":"2493_CR29","doi-asserted-by":"crossref","unstructured":"Hou, X., Oggier, F.: On LCD codes and lattices, Proc. IEEE Int. Symp. on Inform. Theory, 1501\u20131505 (2016)","DOI":"10.1109\/ISIT.2016.7541549"},{"key":"2493_CR30","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.laa.2012.08.010","volume":"430","author":"M Braun","year":"2013","unstructured":"Braun, M., Etzion, T., Vardy, A.: Linearity and complements in projective space. Linear Algebra Appl. 430, 57\u201370 (2013)","journal-title":"Linear Algebra Appl"},{"key":"2493_CR31","doi-asserted-by":"publisher","unstructured":"Crnkovic, V.M., Traunkar, I., Rodrigues, B.G.: LCD codes constructed from weakly p- self-orthogonal 1 designs. Adv. Math. Commun. (2024)https:\/\/doi.org\/10.3934\/amc.2024040","DOI":"10.3934\/amc.2024040"},{"key":"2493_CR32","doi-asserted-by":"publisher","unstructured":"Zoubir, N., Guenda, K., Seneviratne, P.: LCD codes over finite fields, Discrete Mathematics. Algorithms and Applications. https:\/\/doi.org\/10.1142\/s1793830924500708","DOI":"10.1142\/s1793830924500708"},{"key":"2493_CR33","doi-asserted-by":"publisher","unstructured":"Lu, L., Li, R., Ren, Y.: Optimal quaternary hermitian LCD codes. Entropy. 26(5), 373. https:\/\/doi.org\/10.3390\/e26050373. 28 April 2024","DOI":"10.3390\/e26050373"},{"key":"2493_CR34","doi-asserted-by":"crossref","unstructured":"Ghosh, H., Maurya, P.K., Bagchi, S.: Secret Sharing Scheme: Based on LCD Code, 2022 International Interdisciplinary Conference on Mathematics, Engineering and Science (MESIICON), 978\u20131\u20136654\u20137072\u20138\/22, 2022 IEEE.","DOI":"10.1109\/MESIICON55227.2022.10093356"},{"key":"2493_CR35","doi-asserted-by":"crossref","unstructured":"Alahmadi, A., Altassan, A., AlKenani, A., \u00c7alkavur, S., Shoaib, H., Sol\u00e9, P.: A multisecret-sharing scheme based on LCD codes. Mathematics 8(272) (2020)","DOI":"10.3390\/math8020272"},{"key":"2493_CR36","first-page":"175","volume":"32","author":"D Crnkovic","year":"2021","unstructured":"Crnkovic, D., Egan, R., Rodrigues, B.G., Svob, A.: LCD codes from weighing matrices, applicable algebra in engineering. Commun. Comput. 32, 175\u2013189 (2021)","journal-title":"Communication and Computing"},{"issue":"107","key":"2493_CR37","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/0012-365X(92)90563-U","volume":"106","author":"JL Massey","year":"1992","unstructured":"Massey, J.L.: Linear codes with complementary duals. Discrete Math. 106(107), 337\u2013342 (1992)","journal-title":"Discrete Math"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02493-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-025-02493-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02493-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T11:41:19Z","timestamp":1757158879000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-025-02493-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,18]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["2493"],"URL":"https:\/\/doi.org\/10.1007\/s12190-025-02493-1","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,18]]},"assertion":[{"value":"11 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 April 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}