{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T19:19:49Z","timestamp":1773429589217,"version":"3.50.1"},"reference-count":29,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2022]]},"abstract":"<p style='text-indent:20px;'>The notion of an <i>irredundant orthogonal array<\/i> (IrOA) was introduced by Goyeneche and <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\dot{Z} $\\end{document}<\/tex-math><\/inline-formula>yczkowski who showed an IrOA<inline-formula><tex-math id=\"M2\">\\begin{document}$ _{\\lambda}(t, k, v) $\\end{document}<\/tex-math><\/inline-formula> corresponds to a <inline-formula><tex-math id=\"M3\">\\begin{document}$ t $\\end{document}<\/tex-math><\/inline-formula>-uniform state of <inline-formula><tex-math id=\"M4\">\\begin{document}$ k $\\end{document}<\/tex-math><\/inline-formula> subsystems with local dimension <inline-formula><tex-math id=\"M5\">\\begin{document}$ v $\\end{document}<\/tex-math><\/inline-formula> (Physical Review A. 90 (2014), 022316). In this paper, we construct some kinds of 2-uniform states by establishing the existence of IrOA<inline-formula><tex-math id=\"M6\">\\begin{document}$ _{\\lambda}(2, 5, v) $\\end{document}<\/tex-math><\/inline-formula> for any integer <inline-formula><tex-math id=\"M7\">\\begin{document}$ v\\geq 4 $\\end{document}<\/tex-math><\/inline-formula>, <inline-formula><tex-math id=\"M8\">\\begin{document}$ v\\neq 6 $\\end{document}<\/tex-math><\/inline-formula>; IrOA<inline-formula><tex-math id=\"M9\">\\begin{document}$ _{\\lambda}(2, 6, v) $\\end{document}<\/tex-math><\/inline-formula> for any integer <inline-formula><tex-math id=\"M10\">\\begin{document}$ v\\geq 2 $\\end{document}<\/tex-math><\/inline-formula>; IrOA<inline-formula><tex-math id=\"M11\">\\begin{document}$ _{\\lambda}(2, q, q) $\\end{document}<\/tex-math><\/inline-formula> and IrOA<inline-formula><tex-math id=\"M12\">\\begin{document}$ _{\\lambda}(2, q+1, q) $\\end{document}<\/tex-math><\/inline-formula> for any prime power <inline-formula><tex-math id=\"M13\">\\begin{document}$ q &gt;3 $\\end{document}<\/tex-math><\/inline-formula>.<\/p><\/jats:p>","DOI":"10.3934\/amc.2020109","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:40:20Z","timestamp":1600422020000},"page":"231","source":"Crossref","is-referenced-by-count":7,"title":["Further results on 2-uniform states arising from irredundant orthogonal arrays"],"prefix":"10.3934","volume":"16","author":[{"given":"Yajuan","family":"Zang","sequence":"first","affiliation":[]},{"given":"Guangzhou","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Kejun","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Zihong","family":"Tian","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2020109-1","doi-asserted-by":"publisher","unstructured":"R. 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