{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T06:41:05Z","timestamp":1768977665752,"version":"3.49.0"},"reference-count":36,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:p xml:lang=\"fr\">&lt;p style='text-indent:20px;'&gt;For any odd prime &lt;inline-formula&gt;&lt;tex-math id=\"M2\"&gt;\\begin{document}$ p $\\end{document}&lt;\/tex-math&gt;&lt;\/inline-formula&gt;, we study constacyclic codes of length &lt;inline-formula&gt;&lt;tex-math id=\"M3\"&gt;\\begin{document}$ n $\\end{document}&lt;\/tex-math&gt;&lt;\/inline-formula&gt; over the finite commutative non-chain ring &lt;inline-formula&gt;&lt;tex-math id=\"M4\"&gt;\\begin{document}$ R_{k,m} = \\mathbb{F}_{p^m}[u_1,u_2,\\dots,u_k]\/\\langle u^2_i-1,u_iu_j-u_ju_i\\rangle_{i\\neq j = 1,2,\\dots,k} $\\end{document}&lt;\/tex-math&gt;&lt;\/inline-formula&gt;, where &lt;inline-formula&gt;&lt;tex-math id=\"M5\"&gt;\\begin{document}$ m,k\\geq 1 $\\end{document}&lt;\/tex-math&gt;&lt;\/inline-formula&gt; are integers. We determine the necessary and sufficient condition for these codes to contain their Euclidean duals. As an application, from the dual containing constacyclic codes, several MDS, new and better quantum codes compare to the best known codes in the literature are obtained.&lt;\/p&gt;<\/jats:p>","DOI":"10.3934\/amc.2020097","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T11:14:04Z","timestamp":1596453244000},"page":"17","source":"Crossref","is-referenced-by-count":24,"title":["New quantum codes from constacyclic codes over the ring $ R_{k,m} $"],"prefix":"10.3934","volume":"16","author":[{"given":"Habibul","family":"Islam","sequence":"first","affiliation":[]},{"given":"Om","family":"Prakash","sequence":"additional","affiliation":[]},{"given":"Ram Krishna","family":"Verma","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2020097-1","doi-asserted-by":"publisher","unstructured":"M. Ashraf, G. 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Wang, Quantum codes from <inline-formula><tex-math id=\"M1300\">\\begin{document}$(1-2v)$\\end{document}<\/tex-math><\/inline-formula>-constacyclic codes over the ring <inline-formula><tex-math id=\"M1301\">\\begin{document}$\\mathbb{F}_{q}+u\\mathbb{F}_{q}+v\\mathbb{F}_{q}+uv\\mathbb{F}_{q}$\\end{document}<\/tex-math><\/inline-formula>, <i>Discrete Math. Algorithms Appl.<\/i>, <b>10<\/b> (2018), 1850046, 8 pp.","DOI":"10.1142\/S1793830918500465"},{"key":"key-10.3934\/amc.2020097-29","doi-asserted-by":"publisher","unstructured":"F. Ma, J. Gao and F. W. Fu, Constacyclic codes over the ring <inline-formula><tex-math id=\"M1302\">\\begin{document}$\\mathbb{F}_{p} +v\\mathbb{F}_{p}+v^{2}\\mathbb{F}_{p}$\\end{document}<\/tex-math><\/inline-formula> and their applications of constructing new non-binary quantum codes, <i>Quantum Inf. 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