{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T17:38:09Z","timestamp":1770226689970,"version":"3.49.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T00:00:00Z","timestamp":1729209600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T00:00:00Z","timestamp":1729209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Spanish Ministry of Science and innovation through Enabling communication, coding and processing technologies for next-generation classical-quantum networks","award":["PID2022-137099NB-C44"],"award-info":[{"award-number":["PID2022-137099NB-C44"]}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PLEC2021-008251"],"award-info":[{"award-number":["PLEC2021-008251"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010198","name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001870","name":"Fundacja na rzecz Nauki Polskiej","doi-asserted-by":"publisher","award":["ICTQT, contracts no. 2018\/MAB\/5 and 2018\/MAB\/5\/AS-1"],"award-info":[{"award-number":["ICTQT, contracts no. 2018\/MAB\/5 and 2018\/MAB\/5\/AS-1"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2025,1]]},"DOI":"10.1007\/s10623-024-01512-9","type":"journal-article","created":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T15:02:00Z","timestamp":1729263720000},"page":"79-93","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Equivalence of constacyclic codes with shift constants of different orders"],"prefix":"10.1007","volume":"93","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2104-7485","authenticated-orcid":false,"given":"Reza","family":"Dastbasteh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farzad","family":"Padashnick","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro M.","family":"Crespo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Markus","family":"Grassl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javad","family":"Sharafi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,18]]},"reference":[{"issue":"3","key":"1512_CR1","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1007\/s10623-022-01124-1","volume":"91","author":"D Akre","year":"2023","unstructured":"Akre D., Aydin N., Harrington M., Pandey S.: A generalization of cyclic code equivalence algorithm to constacyclic codes. Des. Codes Cryptogr. 91(3), 763\u2013777 (2023).","journal-title":"Des. Codes Cryptogr."},{"issue":"6","key":"1512_CR2","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1109\/TIT.1984.1056973","volume":"30","author":"W Alltop","year":"1984","unstructured":"Alltop W.: A method for extending binary linear codes (corresp.). IEEE Trans. Inf. Theory 30(6), 871\u2013872 (1984).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"1512_CR3","doi-asserted-by":"publisher","first-page":"245","DOI":"10.3934\/amc.2017016","volume":"11","author":"N Aydin","year":"2017","unstructured":"Aydin N., Connolly N., Grassl M.: Some results on the structure of constacyclic codes and new linear codes over $$GF(7)$$ from quasi-twisted codes. Adv. Math. Commun. 11(1), 245\u2013258 (2017).","journal-title":"Adv. Math. Commun."},{"issue":"10","key":"1512_CR4","doi-asserted-by":"publisher","first-page":"2199","DOI":"10.1007\/s10623-019-00613-0","volume":"87","author":"N Aydin","year":"2019","unstructured":"Aydin N., Lambrinos J., VandenBerg O.: On equivalence of cyclic codes, generalization of a quasi-twisted search algorithm, and new linear codes. Des. Codes Cryptogr. 87(10), 2199\u20132212 (2019).","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"1512_CR5","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1023\/A:1013808515797","volume":"25","author":"J Bierbrauer","year":"2002","unstructured":"Bierbrauer J.: The theory of cyclic codes and a generalization to additive codes. Des. Codes Cryptogr. 25(2), 189\u2013206 (2002).","journal-title":"Des. Codes Cryptogr."},{"issue":"1","key":"1512_CR6","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0019-9958(78)90389-3","volume":"37","author":"K Bogart","year":"1978","unstructured":"Bogart K., Goldberg D., Gordon J.: An elementary proof of the MacWilliams theorem on equivalence of codes. Inf. Control 37(1), 19\u201322 (1978).","journal-title":"Inf. Control"},{"issue":"3\u20134","key":"1512_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(3\u20134), 235\u2013265 (1997).","journal-title":"J. Symb. Comput."},{"issue":"4","key":"1512_CR8","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1109\/18.681315","volume":"44","author":"AR Calderbank","year":"1998","unstructured":"Calderbank A.R., Rains E.M., Shor P.W., Sloane N.J.A.: Quantum error correction via codes over $${\\rm GF}(4)$$. IEEE Trans. Inf. Theory 44(4), 1369\u20131387 (1998).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"1512_CR9","doi-asserted-by":"publisher","first-page":"1217","DOI":"10.1016\/j.ffa.2012.10.001","volume":"18","author":"B Chen","year":"2012","unstructured":"Chen B., Fan Y., Lin L., Liu H.: Constacyclic codes over finite fields. Finite Fields Appl. 18(6), 1217\u20131231 (2012).","journal-title":"Finite Fields Appl."},{"issue":"8","key":"1512_CR10","doi-asserted-by":"publisher","first-page":"5253","DOI":"10.1109\/TCOMM.2019.2916085","volume":"67","author":"B Chen","year":"2019","unstructured":"Chen B., Fang W., Xia S.-T., Fu F.-W.: Constructions of optimal (r, $$\\delta $$) locally repairable codes via constacyclic codes. IEEE Trans. Commun. 67(8), 5253\u20135263 (2019).","journal-title":"IEEE Trans. Commun."},{"key":"1512_CR11","doi-asserted-by":"crossref","unstructured":"Dastbasteh R., Lison\u011bk P.: New quantum codes from self-dual codes over $$\\mathbb{F} _4$$. Des. Codes Cryptogr. 1\u201315 (2023).","DOI":"10.1007\/s10623-023-01306-5"},{"issue":"9","key":"1512_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2023.113489","volume":"346","author":"R Dastbasteh","year":"2023","unstructured":"Dastbasteh R., Lison\u011bk P.: On the equivalence of linear cyclic and constacyclic codes. Discret. Math. 346(9), 113489 (2023).","journal-title":"Discret. Math."},{"key":"1512_CR13","doi-asserted-by":"crossref","unstructured":"Ding C., Sun Z., Wang X.: Two classes of constacyclic codes with variable parameters. In: International Workshop on the Arithmetic of Finite Fields, pp. 127\u2013141. Springer, Berlin (2022).","DOI":"10.1007\/978-3-031-22944-2_7"},{"key":"1512_CR14","unstructured":"Grassl M.: Bounds on the minimum distance of linear codes and quantum codes (2007). http:\/\/www.codetables.de. Accessed 26 Feb 2024."},{"issue":"2","key":"1512_CR15","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/0097-3165(93)90043-8","volume":"62","author":"WC Huffman","year":"1993","unstructured":"Huffman W.C., Job V., Pless V.: Multipliers and generalized multipliers of cyclic objects and cyclic codes. J. Comb. Theory Ser. A 62(2), 183\u2013215 (1993).","journal-title":"J. Comb. Theory Ser. A"},{"key":"1512_CR16","volume-title":"The Theory of Error-Correcting Codes","author":"FJ MacWilliams","year":"1977","unstructured":"MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. Elsevier, New York (1977)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-024-01512-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-024-01512-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-024-01512-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T17:11:14Z","timestamp":1737565874000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-024-01512-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,18]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["1512"],"URL":"https:\/\/doi.org\/10.1007\/s10623-024-01512-9","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,18]]},"assertion":[{"value":"27 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 July 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 October 2024","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 that there is no Conflict of interest related to the research presented in the manuscript submitted to Designs, Codes and Cryptography.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}