{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:58:12Z","timestamp":1772283492068,"version":"3.50.1"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,11,21]],"date-time":"2015-11-21T00:00:00Z","timestamp":1448064000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Spanish MICINN grant","award":["TIN2013-40524-P"],"award-info":[{"award-number":["TIN2013-40524-P"]}]},{"name":"Catalan AGAUR grant","award":["2014SGR-691"],"award-info":[{"award-number":["2014SGR-691"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2016,11]]},"DOI":"10.1007\/s10623-015-0163-6","type":"journal-article","created":{"date-parts":[[2015,11,21]],"date-time":"2015-11-21T14:54:26Z","timestamp":1448117666000},"page":"347-364","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Kernels and ranks of cyclic and negacyclic quaternary codes"],"prefix":"10.1007","volume":"81","author":[{"given":"Steven T.","family":"Dougherty","sequence":"first","affiliation":[]},{"given":"Cristina","family":"Fern\u00e1ndez-C\u00f3rdoba","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,21]]},"reference":[{"key":"163_CR1","unstructured":"Blackford T.: Cyclic codes over $${\\mathbb{Z}}_4$$ Z 4 of oddly even length. International Workshop on Coding and Cryptography (WCC 2001) (Paris). Discret. Appl. Math. 128(1), 27\u201346 (2003)."},{"key":"163_CR2","doi-asserted-by":"crossref","unstructured":"Blackford T.: Negacyclic codes over $${\\mathbb{Z}}_4$$ Z 4 of even length. IEEE Trans. Inf. Theory 49(6), 1417\u20131424 (2003).","DOI":"10.1109\/TIT.2003.811915"},{"key":"163_CR3","doi-asserted-by":"crossref","unstructured":"Blackford T.: Negacyclic duadic codes. Finite Fields Appl. 14(4), 930\u2013943 (2008).","DOI":"10.1016\/j.ffa.2008.05.004"},{"key":"163_CR4","doi-asserted-by":"crossref","unstructured":"Borges J., Phelps K.P., Rif\u00e0 J., Zinoviev V.: On $${\\mathbb{Z}}_4$$ Z 4 -linear preparata-like and Kerdock-like. IEEE Tans. Inf. Theory 49(11), 2834\u20132843 (2003).","DOI":"10.1109\/TIT.2003.819329"},{"key":"163_CR5","doi-asserted-by":"crossref","unstructured":"Calderbank A.R., Sloane N.J.A.: Modular and $$p$$ p -adic cyclic codes. Des. Codes Cryptogr. 6(1), 21\u201335 (1995).","DOI":"10.1007\/BF01390768"},{"key":"163_CR6","doi-asserted-by":"crossref","unstructured":"Dougherty S.T., Ling S.: Cyclic codes over $${\\mathbb{Z}}_4$$ Z 4 of even length. Des. Codes Cryptogr. 39(2), 127\u2013153 (2006).","DOI":"10.1007\/s10623-005-2773-x"},{"key":"163_CR7","unstructured":"Fern\u00e1ndez-C\u00f3rdoba C., Pujol J., Villanueva M.: On Rank and Kernel of $${\\mathbb{Z}}_4$$ Z 4 -Linear Codes. Lecture Notes in Computer Science, vol. 5228, pp. 46\u201355. Springer, Berlin (2008)."},{"key":"163_CR8","doi-asserted-by":"crossref","unstructured":"Fern\u00e1ndez-C\u00f3rdoba C., Pujol J., Villanueva M.: $${\\mathbb{Z}}_2{\\mathbb{Z}}_4$$ Z 2 Z 4 -linear codes: rank and kernel. Des. Codes Cryptogr. 56(1), 43\u201359 (2010).","DOI":"10.1007\/s10623-009-9340-9"},{"key":"163_CR9","doi-asserted-by":"crossref","unstructured":"Hammons A.R., Kumar P.V., Calderbank A.R., Sloane N.J.A., Sol\u00e9 P.: The $${\\mathbb{Z}}_4$$ Z 4 -linearity of Kerdock, Preparata, Goethals and related codes. IEEE Trans. Inf. Theory 40(2), 301\u2013319 (1994).","DOI":"10.1109\/18.312154"},{"key":"163_CR10","doi-asserted-by":"crossref","unstructured":"Pless V.S., Qian Z.: Cyclic codes and quadratic residue codes over $${\\mathbb{Z}}_4$$ Z 4 . IEEE Trans. Inf. Theory 42(5), 1594\u20131600 (1996).","DOI":"10.1109\/18.532906"},{"key":"163_CR11","doi-asserted-by":"crossref","unstructured":"Pless V.S., Sol\u00e9 P., Qian Z.: Cyclic self-dual $${\\mathbb{Z}}_4$$ Z 4 -codes. Finite Field Appl. 3(1), 48\u201369 (1997).","DOI":"10.1006\/ffta.1996.0172"},{"key":"163_CR12","doi-asserted-by":"crossref","unstructured":"Wolfmann J.: Binary images of cyclic codes over $${\\mathbb{Z}}_4$$ Z 4 . IEEE Tans. Inf. Theory 47(5), 1773\u20131779 (2001).","DOI":"10.1109\/18.930917"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-015-0163-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-015-0163-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-015-0163-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T19:58:41Z","timestamp":1559246321000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-015-0163-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,21]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,11]]}},"alternative-id":["163"],"URL":"https:\/\/doi.org\/10.1007\/s10623-015-0163-6","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,21]]}}}