{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:14:27Z","timestamp":1773231267143,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a well-known result for linear codes over fields, we prove that there exists a one-to-one correspondence between so-called fat linear codes over chain rings and multisets of points in projective Hjelmslev geometries, in the sense that semilinearly isomorphic codes correspond to equivalent multisets and vice versa. Using a selected class of multisets we show that certain MacDonald codes are linearly representable over nontrivial chain rings.<\/jats:p>","DOI":"10.37236\/1489","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:05:48Z","timestamp":1578708348000},"source":"Crossref","is-referenced-by-count":51,"title":["Linear Codes over Finite Chain Rings"],"prefix":"10.37236","volume":"7","author":[{"given":"Thomas","family":"Honold","sequence":"first","affiliation":[]},{"given":"Ivan","family":"Landjev","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,12,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:31:45Z","timestamp":1579325505000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,12,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1489","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,12,18]]},"article-number":"R11"}}