{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T04:43:29Z","timestamp":1774154609824,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T00:00:00Z","timestamp":1726358400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T00:00:00Z","timestamp":1726358400000},"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":[[2026,1]]},"DOI":"10.1007\/s00200-024-00668-0","type":"journal-article","created":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T15:02:06Z","timestamp":1726412526000},"page":"73-93","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Double skew cyclic codes over $$\\mathbb {F}_q+v\\mathbb {F}_q$$"],"prefix":"10.1007","volume":"37","author":[{"given":"Ashutosh","family":"Singh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tulay","family":"Yildirim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Om","family":"Prakash","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,9,15]]},"reference":[{"issue":"2","key":"668_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-020-02977-y","volume":"20","author":"A Alahmadi","year":"2021","unstructured":"Alahmadi, A., Islam, H., Prakash, O., Sol\u00e9, P., Alkenani, A., Muthana, N., Hijazi, R.: New quantum codes from constacyclic codes over a non-chain ring. Quantum Inf. Process. 20(2), 1\u201317 (2021)","journal-title":"Quantum Inf. Process."},{"key":"668_CR2","unstructured":"Ayats, J.B., Fern\u00e1ndez-C\u00f3rdoba, C., Ten-Valls, R.: $$\\mathbb{Z}_2$$-double cyclic codes. Organizadas por el Grupo de Matem\u00e1tica Discreta de la Universitat Rovira i Virgili 139 (2014). http:\/\/deim.urv.cat\/discrete-math\/RGoDM"},{"issue":"3","key":"668_CR3","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/s40314-022-01833-2","volume":"41","author":"I Aydogdu","year":"2022","unstructured":"Aydogdu, I., Hesari, R.M., Samei, K.: Double skew cyclic codes over $$\\mathbb{F}_q$$. Comput. Appl. Math. 41(3), 126 (2022)","journal-title":"Comput. Appl. Math."},{"issue":"2","key":"668_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40314-021-01428-3","volume":"40","author":"S Bathala","year":"2021","unstructured":"Bathala, S., Seneviratne, P.: Some results on $$\\mathbb{F} _4[v]$$-double cyclic codes. Comput. Appl. Math. 40(2), 1\u201317 (2021)","journal-title":"Comput. Appl. Math."},{"issue":"4","key":"668_CR5","doi-asserted-by":"publisher","first-page":"1250","DOI":"10.1109\/18.761278","volume":"45","author":"A Bonnecaze","year":"1999","unstructured":"Bonnecaze, A., Udaya, P.: Cyclic codes and self dual codes over $$\\mathbb{F} _2 +u\\mathbb{F} _2$$. IEEE Trans. Inform. Theory 45(4), 1250\u20131255 (1999)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"668_CR6","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s10623-017-0334-8","volume":"86","author":"J Borges","year":"2018","unstructured":"Borges, J., Fernandez-C\u00f3rdoba, C., Ten-Valls, R.: $$\\mathbb{Z} _2$$-double cyclic codes. Des. Codes Cryptogr. 86(3), 463\u2013479 (2018)","journal-title":"Des. Codes Cryptogr."},{"key":"668_CR7","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: the user language. J. Symb. Comput. 24, 235\u2013265 (1997)","journal-title":"J. Symb. Comput."},{"issue":"4","key":"668_CR8","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s00200-007-0043-z","volume":"18","author":"D Boucher","year":"2007","unstructured":"Boucher, D., Geiselmann, W., Ulmer, F.: Skew cyclic codes. Appl. Algebra Eng. Commun. Comput. 18(4), 379\u2013389 (2007)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"668_CR9","doi-asserted-by":"crossref","unstructured":"Boucher, D., Ulmer, F.: A note on the dual codes of module skew codes. In: Lecture Notes in Computer Science, vol. 7089, 230-243. Springer, Berlin (2011)","DOI":"10.1007\/978-3-642-25516-8_14"},{"issue":"10","key":"668_CR10","doi-asserted-by":"publisher","first-page":"1820","DOI":"10.3390\/math8101820","volume":"8","author":"T Deng","year":"2020","unstructured":"Deng, T., Yang, J.: Double cyclic codes over $$\\mathbb{F} _q+v\\mathbb{F} _q$$. Mathematics 8(10), 1820 (2020)","journal-title":"Mathematics"},{"key":"668_CR11","first-page":"1672","volume":"31","author":"YL Diao","year":"2017","unstructured":"Diao, Y.L., Gao, J.: Double cyclic codes over finite fields. J. Shandong Univ. Tech. (Nat. Sci.) 31, 1672\u20136197 (2017)","journal-title":"J. Shandong Univ. Tech. (Nat. Sci.)"},{"key":"668_CR12","doi-asserted-by":"crossref","unstructured":"Dougherty, S.T., Korban, A., \u015fahinkaya, S.: Self-dual additive codes. Appl. Algebra Eng. Commun. Comput. 33(5), 569\u2013586 (2022)","DOI":"10.1007\/s00200-020-00473-5"},{"issue":"2","key":"668_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s00200-018-0366-y","volume":"30","author":"Y Gao","year":"2019","unstructured":"Gao, Y., Gao, J., Fu, F.W.: Quantum codes from cyclic codes over the ring $$\\mathbb{F} _q+ v_1 \\mathbb{F} _q+\\cdots + v_r \\mathbb{F} _q$$. Appl. Algebra Eng. Commun. Comput. 30(2), 161\u2013174 (2019)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"key":"668_CR14","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/j.ffa.2016.02.003","volume":"39","author":"J Gao","year":"2016","unstructured":"Gao, J., Shi, M.J., Wu, T.T.: On double cyclic codes over $$\\mathbb{Z} _4$$. Finite Fields Appl. 39, 233\u2013250 (2016)","journal-title":"Finite Fields Appl."},{"key":"668_CR15","unstructured":"Grassl, M.: Table of bounds on linear codes. (2007). http:\/\/www.codetables.de\/. Accessed 08 July 2024"},{"issue":"3","key":"668_CR16","doi-asserted-by":"publisher","first-page":"313","DOI":"10.3934\/amc.2014.8.313","volume":"8","author":"F Gursoy","year":"2014","unstructured":"Gursoy, F., Siap, I., Yildiz, B.: Construction of skew cyclic codes over $$\\mathbb{F} _q+v\\mathbb{F} _q$$. Adv. Math. Commun. 8(3), 313\u2013322 (2014)","journal-title":"Adv. Math. Commun."},{"key":"668_CR17","volume-title":"Finite rings with identity","author":"BR McDonald","year":"1974","unstructured":"McDonald, BR.: Finite rings with identity. Marcel Dekker (1974)"},{"issue":"3","key":"668_CR18","doi-asserted-by":"publisher","first-page":"480","DOI":"10.2307\/1968173","volume":"34","author":"O Ore","year":"1933","unstructured":"Ore, O.: Theory of noncommutative polynomials. Ann. Math. 34(3), 480\u2013508 (1933)","journal-title":"Ann. Math."},{"issue":"5","key":"668_CR19","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1007\/s12095-022-00572-9","volume":"14","author":"S Patel","year":"2022","unstructured":"Patel, S., Prakash, O., Islam, H.: Cyclic codes over $$M_4(\\mathbb{F} _2+u\\mathbb{F} _2)$$. Cryptogr. Commun. 14(5), 1021\u20131034 (2022)","journal-title":"Cryptogr. Commun."},{"issue":"1","key":"668_CR20","first-page":"10","volume":"2","author":"I Siap","year":"2011","unstructured":"Siap, I., Abualrub, T., Aydin, N., Seneviratne, P.: Skew cyclic codes of arbitrary length. Int. J. Inf. Coding Theory 2(1), 10\u201320 (2011)","journal-title":"Int. J. Inf. Coding Theory"},{"issue":"1","key":"668_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10623-013-9843-2","volume":"74","author":"AK Singh","year":"2015","unstructured":"Singh, A.K., Kewat, P.K.: On cyclic codes over the ring $$\\mathbb{Z} _p[u]\/ {\\langle } u^k {\\rangle }$$. Des. Codes Cryptogr. 74(1), 1\u201313 (2015)","journal-title":"Des. Codes Cryptogr."},{"key":"668_CR22","first-page":"1672","volume":"32","author":"YK Wang","year":"2018","unstructured":"Wang, Y.K., Gao, J.: Double $$\\lambda$$-constacyclic codes over finite chain rings. J. Shandong Univ. Tech. (Nat. Sci.) 32, 1672\u20136197 (2018)","journal-title":"J. Shandong Univ. Tech. (Nat. Sci.)"},{"key":"668_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/s13226-023-00451-w","author":"T Yildirim","year":"2023","unstructured":"Yildirim, T.: Construction of cyclic DNA codes over $$\\mathbb{Z} _4\\mathbb{R}$$. Indian J. Pure Appl. Math. (2023). https:\/\/doi.org\/10.1007\/s13226-023-00451-w","journal-title":"Indian J. Pure Appl. Math."},{"issue":"4","key":"668_CR24","first-page":"226","volume":"2","author":"B Yildiz","year":"2014","unstructured":"Yildiz, B., Aydin, N.: On cyclic codes over $$\\mathbb{Z} _4 + u\\mathbb{Z} _4$$ and $$\\mathbb{Z} _4$$ images. Int. J. Inf. Coding Theory 2(4), 226\u2013237 (2014)","journal-title":"Int. J. Inf. Coding Theory"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-024-00668-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-024-00668-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-024-00668-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T07:14:35Z","timestamp":1767942875000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-024-00668-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,15]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["668"],"URL":"https:\/\/doi.org\/10.1007\/s00200-024-00668-0","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,15]]},"assertion":[{"value":"11 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 September 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}