{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T22:49:26Z","timestamp":1761864566485,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T00:00:00Z","timestamp":1694736000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T00:00:00Z","timestamp":1694736000000},"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":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2023,10]]},"DOI":"10.1007\/s12190-023-01914-3","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T09:06:00Z","timestamp":1694768760000},"page":"4023-4043","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Construction methods for Galois LCD codes over finite fields"],"prefix":"10.1007","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5872-7702","authenticated-orcid":false,"given":"Gyanendra K.","family":"Verma","sequence":"first","affiliation":[]},{"given":"Astha","family":"Agrawal","sequence":"additional","affiliation":[]},{"given":"R. K.","family":"Sharma","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"1914_CR1","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/0012-365X(92)90563-U","volume":"106\u2013107","author":"JL Massey","year":"1992","unstructured":"Massey, J.L.: Linear codes with complementary duals. Discrete Math. 106\u2013107, 337\u2013342 (1992)","journal-title":"Discrete Math."},{"key":"1914_CR2","doi-asserted-by":"publisher","first-page":"131","DOI":"10.3934\/amc.2016.10.131","volume":"10","author":"C Carlet","year":"2016","unstructured":"Carlet, C., Guilley, S.: Complementary dual codes for counter-measures to side-channel attacks. Adv. Math. Commun. 10, 131\u2013150 (2016)","journal-title":"Adv. Math. Commun."},{"key":"1914_CR3","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s10623-017-0330-z","volume":"86","author":"K Guenda","year":"2016","unstructured":"Guenda, K., Jitman, S., Gulliver, T.A.: Constructions of good entanglement-assisted quantum error correcting codes. Des. Codes Cryptogr. 86, 121\u2013136 (2016)","journal-title":"Des. Codes Cryptogr."},{"key":"1914_CR4","doi-asserted-by":"publisher","first-page":"3077","DOI":"10.1007\/s10623-019-00664-3","volume":"87","author":"Z Liu","year":"2019","unstructured":"Liu, Z., Wang, J.: Linear complementary dual codes over rings. Des. Codes Cryptogr. 87, 3077\u20133086 (2019)","journal-title":"Des. Codes Cryptogr."},{"key":"1914_CR5","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1109\/LCOMM.2020.3029073","volume":"25","author":"Z Liu","year":"2021","unstructured":"Liu, Z., Wu, X.: Notes on LCD codes over frobenius rings. IEEE Commun. Lett. 25, 361\u2013364 (2021)","journal-title":"IEEE Commun. Lett."},{"key":"1914_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ffa.2015.01.004","volume":"34","author":"X Liu","year":"2015","unstructured":"Liu, X., Liu, H.: LCD codes over finite chain rings. Finite Fields Their Appl. 34, 1\u201319 (2015)","journal-title":"Finite Fields Their Appl."},{"key":"1914_CR7","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1017\/S0004972722001344","volume":"107","author":"A Agrawal","year":"2023","unstructured":"Agrawal, A., Verma, G.K., Sharma, R.K.: Galois LCD codes over $$\\mathbb{F} _q +u\\mathbb{F} _q +v\\mathbb{F} _q +uv\\mathbb{F} _q$$. Bull. Austral. Math. Soc. 107, 330\u2013341 (2023). https:\/\/doi.org\/10.1017\/S0004972722001344","journal-title":"Bull. Austral. Math. Soc."},{"issue":"1","key":"1914_CR8","doi-asserted-by":"publisher","first-page":"139","DOI":"10.3934\/amc.2021070","volume":"17","author":"K Ishizuka","year":"2023","unstructured":"Ishizuka, K., Saito, K.: Construction for both self-dual codes and lcd codes. Adv. Math. Commun. 17(1), 139\u2013151 (2023)","journal-title":"Adv. Math. Commun."},{"key":"1914_CR9","unstructured":"Li, S., Shi, M.: Improved lower and upper bounds for LCD codes. arXiv:2206.04936 (2022)"},{"key":"1914_CR10","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s10623-016-0282-8","volume":"84","author":"Y Fan","year":"2017","unstructured":"Fan, Y., Zhang, L.: Galois self-dual constacyclic codes. Des. Codes Cryptogr. 84, 473\u2013492 (2017)","journal-title":"Des. Codes Cryptogr."},{"key":"1914_CR11","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/j.ffa.2017.10.001","volume":"49","author":"X Liu","year":"2018","unstructured":"Liu, X., Fan, Y., Liu, H.: Galois LCD codes over finite fields. Finite Fields Their Appl. 49, 227\u2013242 (2018)","journal-title":"Finite Fields Their Appl."},{"key":"1914_CR12","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s10623-019-00681-2","volume":"88","author":"H Liu","year":"2020","unstructured":"Liu, H., Pan, X.: Galois hulls of linear codes over finite fields. Des. Codes Cryptogr. 88, 241\u2013255 (2020)","journal-title":"Des. Codes Cryptogr."},{"key":"1914_CR13","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s12095-022-00591-6","volume":"15","author":"I Debnath","year":"2022","unstructured":"Debnath, I., Prakash, O., Islam, H.: Galois hulls of constacyclic codes over finite fields. Cryptogr. Commun. 15, 111\u2013127 (2022)","journal-title":"Cryptogr. Commun."},{"issue":"3","key":"1914_CR14","doi-asserted-by":"publisher","first-page":"1694","DOI":"10.1109\/TIT.2018.2873130","volume":"65","author":"C Carlet","year":"2019","unstructured":"Carlet, C., Mesnager, S., Tang, C., Qi, Y.: On $$\\sigma $$ -lcd codes. IEEE Trans. Inf. Theory 65(3), 1694\u20131704 (2019). https:\/\/doi.org\/10.1109\/TIT.2018.2873130","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1914_CR15","doi-asserted-by":"crossref","unstructured":"Liu, X., Liu, H., Yu, L.: New EAQEC codes constructed from galois lcd codes. Quantum Inf. Process. 19 (2019)","DOI":"10.1007\/s11128-019-2515-z"},{"key":"1914_CR16","doi-asserted-by":"crossref","unstructured":"Hu, P., Liu, X.: Three classes of new EAQEC MDS codes. Quantum Inf. Process. 20 (2021)","DOI":"10.1007\/s11128-021-03039-7"},{"key":"1914_CR17","doi-asserted-by":"publisher","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24(3-4), 235\u2013265 (1997). https:\/\/doi.org\/10.1006\/jsco.1996.0125","DOI":"10.1006\/jsco.1996.0125"},{"key":"1914_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2021.101950","volume":"77","author":"S Talbi","year":"2022","unstructured":"Talbi, S., Batoul, A., Tabue, A.F., Mart\u2019inez-Moro, E.: Galois hulls of cyclic serial codes over a finite chain ring. Finite Fields Their Appl. 77, 101950 (2022)","journal-title":"Finite Fields Their Appl."},{"key":"1914_CR19","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s12190-019-01286-7","volume":"62","author":"S Thipworawimon","year":"2019","unstructured":"Thipworawimon, S., Jitman, S.: Hulls of linear codes revisited with applications. J. Appl. Math. Comput. 62, 325\u2013340 (2019)","journal-title":"J. Appl. Math. Comput."},{"key":"1914_CR20","doi-asserted-by":"publisher","first-page":"7964","DOI":"10.1109\/TIT.2021.3117562","volume":"67","author":"M Cao","year":"2021","unstructured":"Cao, M.: MDS codes with galois hulls of arbitrary dimensions and the related entanglement-assisted quantum error correction. IEEE Trans. Inf. Theory 67, 7964\u20137984 (2021)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"1914_CR21","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1007\/s00200-020-00473-5","volume":"33","author":"ST Dougherty","year":"2022","unstructured":"Dougherty, S.T., Korban, A., \u015eahinkaya, S.: Self-dual additive codes. Appl. Algebra Eng. Commun. Comput. 33(5), 569\u2013586 (2022). https:\/\/doi.org\/10.1007\/s00200-020-00473-5","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"1914_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2021.101925","volume":"76","author":"M Araya","year":"2021","unstructured":"Araya, M., Harada, M., Saito, K.: On the minimum weights of binary LCD codes and ternary LCD codes. Finite Fields Appl 76, 101925 (2021). https:\/\/doi.org\/10.1016\/j.ffa.2021.101925","journal-title":"Finite Fields Appl"},{"issue":"1","key":"1914_CR23","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.disc.2018.09.034","volume":"342","author":"M Araya","year":"2019","unstructured":"Araya, M., Harada, M.: On the classification of linear complementary dual codes. Discrete Math. 342(1), 270\u2013278 (2019). https:\/\/doi.org\/10.1016\/j.disc.2018.09.034","journal-title":"Discrete Math."},{"key":"1914_CR24","unstructured":"Grassl, M.: Bounds on the minimum distance of linear codes and quantum codes. Online available at. http:\/\/www.codetables.de"},{"issue":"10","key":"1914_CR25","doi-asserted-by":"publisher","first-page":"2295","DOI":"10.1007\/s10623-021-00916-1","volume":"89","author":"M Harada","year":"2021","unstructured":"Harada, M.: Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes. Des. Codes Cryptogr. 89(10), 2295\u20132312 (2021). https:\/\/doi.org\/10.1007\/s10623-021-00916-1","journal-title":"Des. Codes Cryptogr."},{"key":"1914_CR26","unstructured":"Betten, A., Braun, M., Fripertinger, H., Kerber, A., Kohnert, A., Wassermann, A.: Error-correcting linear codes: classification by isometry and applications (2006)"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01914-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-023-01914-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01914-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T14:35:46Z","timestamp":1695825346000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-023-01914-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,15]]},"references-count":26,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["1914"],"URL":"https:\/\/doi.org\/10.1007\/s12190-023-01914-3","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2023,9,15]]},"assertion":[{"value":"16 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 September 2023","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 have no conflicts of interest in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}