{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T03:02:14Z","timestamp":1774580534957,"version":"3.50.1"},"reference-count":13,"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":[[2014,6]]},"abstract":"<jats:p> Linear codes constitute an important family of error-correcting codes and have a rich algebraic structure. Initially, these codes were studied with respect to the Hamming metric; while for the past few years, they are also studied with respect to a non-Hamming metric, known as the Rosenbloom\u2013Tsfasman metric (also known as RT metric or \u03c1 metric). In this paper, we introduce and study the split \u03c1 weight enumerator of a linear code in the R-module M<jats:sub>n\u00d7s<\/jats:sub>(R) of all n \u00d7 s matrices over R, where R is a finite Frobenius commutative ring with unity. We also define the Lee complete \u03c1 weight enumerator of a linear code in M<jats:sub>n\u00d7s<\/jats:sub>(\u2124<jats:sub>k<\/jats:sub>), where \u2124<jats:sub>k<\/jats:sub> is the ring of integers modulo k \u2265 2. We also derive the MacWilliams identities for each of these \u03c1 weight enumerators. <\/jats:p>","DOI":"10.1142\/s179383091450030x","type":"journal-article","created":{"date-parts":[[2014,2,10]],"date-time":"2014-02-10T07:38:11Z","timestamp":1392017891000},"page":"1450030","source":"Crossref","is-referenced-by-count":5,"title":["MACWILLIAMS IDENTITIES FOR WEIGHT ENUMERATORS WITH RESPECT TO THE RT METRIC"],"prefix":"10.1142","volume":"06","author":[{"given":"AMIT K.","family":"SHARMA","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India"}]},{"given":"ANURADHA","family":"SHARMA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India"}]}],"member":"219","published-online":{"date-parts":[[2014,3,19]]},"reference":[{"key":"rf1","first-page":"83","volume":"2","author":"Dougherty S. T.","journal-title":"Moscow Math. J."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1020834531372"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.3923\/itj.2012.1770.1775"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755279"},{"key":"rf5","first-page":"25","volume":"5","author":"Ozen M.","journal-title":"Selcuk J. Appl. Math."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-004-5658-5"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2006.02.001"},{"key":"rf8","first-page":"45","volume":"33","author":"Rosenbloom M. Yu.","journal-title":"Probl. Inf. Transm."},{"key":"rf10","first-page":"465","volume":"26","author":"Siap I.","journal-title":"Turkish J. Math."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(04)90013-4"},{"key":"rf12","first-page":"301","volume":"13","author":"Skriganov M. M.","journal-title":"St. Petersburg Math. J."},{"key":"rf13","first-page":"1075","volume":"38","author":"Xu H.","journal-title":"J. Univ. Sci. Technol. China"},{"key":"rf14","first-page":"107","volume":"26","author":"Zhu S.","journal-title":"J. Appl. Math. Informatics"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383091450030X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:44:41Z","timestamp":1565192681000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383091450030X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,19]]},"references-count":13,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,3,19]]},"published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.1142\/S179383091450030X"],"URL":"https:\/\/doi.org\/10.1142\/s179383091450030x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,19]]}}}