{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:03:06Z","timestamp":1772283786581,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2016,6]]},"abstract":"<jats:p> In this paper, we study some structural properties of [Formula: see text]-additive cyclic codes in [Formula: see text] as [Formula: see text]-submodules of [Formula: see text], where [Formula: see text]. The generators for these codes are obtained and a minimal spanning set is determined for even and odd [Formula: see text] separately with arbitrary [Formula: see text]. We also determine the generators of duals of the [Formula: see text]-additive cyclic codes for odd [Formula: see text]. A necessary condition for a 1-generator [Formula: see text]-cyclic code to be a [Formula: see text]-free module is obtained. <\/jats:p>","DOI":"10.1142\/s1793830916500270","type":"journal-article","created":{"date-parts":[[2016,2,16]],"date-time":"2016-02-16T09:54:18Z","timestamp":1455616458000},"page":"1650027","source":"Crossref","is-referenced-by-count":10,"title":["\u21242(\u21242 + u\u21242)-Additive cyclic codes and their duals"],"prefix":"10.1142","volume":"08","author":[{"given":"B","family":"Srinivasulu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maheshanand","family":"Bhaintwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,5,26]]},"reference":[{"key":"S1793830916500270BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-006-9034-5"},{"key":"S1793830916500270BIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2013.859854"},{"key":"S1793830916500270BIB003","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2299791"},{"key":"S1793830916500270BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-009-0110-8"},{"key":"S1793830916500270BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/18.761278"},{"key":"S1793830916500270BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-009-9316-9"},{"key":"S1793830916500270BIB010","doi-asserted-by":"publisher","DOI":"10.1109\/18.720545"},{"key":"S1793830916500270BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/18.904544"},{"key":"S1793830916500270BIB012","doi-asserted-by":"publisher","DOI":"10.1109\/18.312154"},{"key":"S1793830916500270BIB013","volume-title":"The Theory of Error Correcting Codes","author":"MacWilliams F. J.","year":"1977"},{"key":"S1793830916500270BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2011.10.020"},{"key":"S1793830916500270BIB015","first-page":"24","volume":"5","author":"Siap I.","year":"2005","journal-title":"Appl. Math. E-Notes"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830916500270","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:04:42Z","timestamp":1565139882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830916500270"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,26]]},"references-count":12,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2016,5,26]]},"published-print":{"date-parts":[[2016,6]]}},"alternative-id":["10.1142\/S1793830916500270"],"URL":"https:\/\/doi.org\/10.1142\/s1793830916500270","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,26]]}}}