{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T22:40:38Z","timestamp":1649025638821},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,10]]},"abstract":"<jats:p> Self-dual and maximal self-orthogonal codes over [Formula: see text], where [Formula: see text] is even or [Formula: see text](mod 4), are extensively studied in this paper. We prove that every maximal self-orthogonal code can be extended to a self-dual code as in the case of binary Golay code. Using these results, we show that a self-dual code can also be constructed by gluing theory even if the sum of the lengths of the gluing components is odd. Furthermore, the (Hamming) weight enumerator [Formula: see text] of a self-dual code [Formula: see text] is given in terms of a maximal self-orthogonal code [Formula: see text], where [Formula: see text] is obtained by the extension of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830919500526","type":"journal-article","created":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T22:10:41Z","timestamp":1565647841000},"page":"1950052","source":"Crossref","is-referenced-by-count":0,"title":["Extended maximal self-orthogonal codes"],"prefix":"10.1142","volume":"11","author":[{"given":"Yilmaz","family":"Dur\u011fun","sequence":"first","affiliation":[{"name":"Department of Mathematics, \u00c7ukurova University, 01330, Adana, Turkey"}]}],"member":"219","published-online":{"date-parts":[[2019,11,3]]},"reference":[{"key":"S1793830919500526BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(80)90057-6"},{"key":"S1793830919500526BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1979.1056047"},{"key":"S1793830919500526BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00389-8"},{"key":"S1793830919500526BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807077"},{"key":"S1793830919500526BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1779-2"},{"key":"S1793830919500526BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(82)90019-X"},{"key":"S1793830919500526BIB007","doi-asserted-by":"publisher","DOI":"10.1137\/0131058"},{"key":"S1793830919500526BIB008","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2010.4.579"},{"key":"S1793830919500526BIB009","volume-title":"Self-dual Codes and Invariant Theory","volume":"17","author":"Nebe G.","year":"2006"},{"key":"S1793830919500526BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(68)80067-5"},{"key":"S1793830919500526BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1987.1057345"},{"key":"S1793830919500526BIB012","first-page":"177","volume-title":"Handbook of Coding Theory","author":"Rains E. M.","year":"1998"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500526","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T01:15:25Z","timestamp":1572830125000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500526"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10]]},"references-count":12,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["10.1142\/S1793830919500526"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500526","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10]]}}}