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In this paper, we present a construction of some families of rotated <inline-formula><tex-math id=\"M2\">\\begin{document}$ A_n- $\\end{document}<\/tex-math><\/inline-formula>lattices, for <inline-formula><tex-math id=\"M3\">\\begin{document}$ n = 2^{r-2}-1 $\\end{document}<\/tex-math><\/inline-formula>, <inline-formula><tex-math id=\"M4\">\\begin{document}$ r \\geq 4 $\\end{document}<\/tex-math><\/inline-formula>, via totally real subfield of cyclotomic fields. Furthermore, closed-form expressions for the minimum product distance of those lattices are obtained through algebraic properties.<\/p><\/jats:p>","DOI":"10.3934\/amc.2020118","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T09:28:10Z","timestamp":1605864490000},"page":"439","source":"Crossref","is-referenced-by-count":0,"title":["Rotated $ A_n $-lattice codes of full diversity"],"prefix":"10.3934","volume":"16","author":[{"given":"Agnaldo Jos\u00e9","family":"Ferrari","sequence":"first","affiliation":[{"name":"School of Sciences, Department of Mathematics, S\u00e3o Paulo State University - UNESP, Bauru, SP 17033-360, BR"}]},{"given":"Tatiana Miguel Rodrigues","family":"de Souza","sequence":"additional","affiliation":[{"name":"School of Sciences, Department of Mathematics, S\u00e3o Paulo State University - UNESP, Bauru, SP 17033-360, BR"}]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2020118-1","doi-asserted-by":"publisher","unstructured":"E. 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