{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:00Z","timestamp":1740155940615,"version":"3.37.3"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,4]]},"abstract":"<jats:p> We study about monotonicity of [Formula: see text]-identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube. Also, we give the lower bounds for [Formula: see text] where [Formula: see text] is the smallest cardinality among all [Formula: see text]-identifying codes in [Formula: see text] with respect to the Lee metric. We prove the existence of [Formula: see text]-identifying code in an incomplete hypercube. Also, we give the construction techniques for [Formula: see text]-identifying codes in the incomplete hypercubes in Secs. 4.1 and 4.2. Using these techniques, we give the tables (see Tables 1\u20136) of upper bounds for [Formula: see text] where [Formula: see text] is the smallest cardinality among all [Formula: see text]-identifying codes in an incomplete hypercube with [Formula: see text] processors. Also, we give the exact values of [Formula: see text] for small values of [Formula: see text] and [Formula: see text] (see Sec. 4.3). <\/jats:p>","DOI":"10.1142\/s1793830919500277","type":"journal-article","created":{"date-parts":[[2019,2,25]],"date-time":"2019-02-25T21:34:25Z","timestamp":1551130465000},"page":"1950027","source":"Crossref","is-referenced-by-count":3,"title":["r-Identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube"],"prefix":"10.1142","volume":"11","author":[{"given":"R.","family":"Dhanalakshmi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu 620024, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0235-3611","authenticated-orcid":false,"given":"C.","family":"Durairajan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu 620024, India"}]}],"member":"219","published-online":{"date-parts":[[2019,4,24]]},"reference":[{"key":"S1793830919500277BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00113-3"},{"key":"S1793830919500277BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01204731"},{"key":"S1793830919500277BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.03.032"},{"key":"S1793830919500277BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/40.127581"},{"key":"S1793830919500277BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.09.002"},{"key":"S1793830919500277BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/MM.1986.304707"},{"key":"S1793830919500277BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00236-002-0093-4"},{"volume-title":"Parallel Supercomputing in MIMD Architectures","year":"1993","author":"Hord R. M.","key":"S1793830919500277BIB008"},{"key":"S1793830919500277BIB010","doi-asserted-by":"publisher","DOI":"10.1109\/18.661507"},{"key":"S1793830919500277BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/12.4611"},{"key":"S1793830919500277BIB012","first-page":"93","volume":"59","author":"Kim J. L.","year":"2010","journal-title":"Bull. Inst. Combin. Appl."},{"key":"S1793830919500277BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.928263"},{"key":"S1793830919500277BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2005.05.030"},{"key":"S1793830919500277BIB015","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511808968"},{"key":"S1793830919500277BIB016","doi-asserted-by":"publisher","DOI":"10.1109\/71.508253"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500277","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:31:12Z","timestamp":1565105472000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500277"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4]]},"references-count":15,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2019,4,24]]},"published-print":{"date-parts":[[2019,4]]}},"alternative-id":["10.1142\/S1793830919500277"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500277","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2019,4]]}}}