{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T09:40:50Z","timestamp":1656495650578},"reference-count":42,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2022]]},"abstract":"<p style='text-indent:20px;'>Cyclotomy, firstly introduced by Gauss, is an important topic in Mathematics since it has a number of applications in number theory, combinatorics, coding theory and cryptography. Depending on <inline-formula><tex-math id=\"M2\">\\begin{document}$ v $\\end{document}<\/tex-math><\/inline-formula> prime or composite, cyclotomy on a residue class ring <inline-formula><tex-math id=\"M3\">\\begin{document}$ {\\mathbb{Z}}_{v} $\\end{document}<\/tex-math><\/inline-formula> can be divided into classical cyclotomy or generalized cyclotomy. Inspired by a foregoing work of Zeng et al. [<xref ref-type=\"bibr\" rid=\"b40\">40<\/xref>], we introduce a generalized cyclotomy of order <inline-formula><tex-math id=\"M4\">\\begin{document}$ e $\\end{document}<\/tex-math><\/inline-formula> on the ring <inline-formula><tex-math id=\"M5\">\\begin{document}$ {\\rm GF}(q_1)\\times {\\rm GF}(q_2)\\times \\cdots \\times {\\rm GF}(q_k) $\\end{document}<\/tex-math><\/inline-formula>, where <inline-formula><tex-math id=\"M6\">\\begin{document}$ q_i $\\end{document}<\/tex-math><\/inline-formula> and <inline-formula><tex-math id=\"M7\">\\begin{document}$ q_j $\\end{document}<\/tex-math><\/inline-formula> (<inline-formula><tex-math id=\"M8\">\\begin{document}$ i\\neq j $\\end{document}<\/tex-math><\/inline-formula>) may not be co-prime, which includes classical cyclotomy as a special case. Here, <inline-formula><tex-math id=\"M9\">\\begin{document}$ q_1 $\\end{document}<\/tex-math><\/inline-formula>, <inline-formula><tex-math id=\"M10\">\\begin{document}$ q_2 $\\end{document}<\/tex-math><\/inline-formula>, <inline-formula><tex-math id=\"M11\">\\begin{document}$ \\cdots $\\end{document}<\/tex-math><\/inline-formula>, <inline-formula><tex-math id=\"M12\">\\begin{document}$ q_k $\\end{document}<\/tex-math><\/inline-formula> are powers of primes with an integer <inline-formula><tex-math id=\"M13\">\\begin{document}$ e|(q_i-1) $\\end{document}<\/tex-math><\/inline-formula> for any <inline-formula><tex-math id=\"M14\">\\begin{document}$ 1\\leq i\\leq k $\\end{document}<\/tex-math><\/inline-formula>. Then we obtain some basic properties of the corresponding generalized cyclotomic numbers. Furthermore, we propose three classes of partitioned difference families by means of the generalized cyclotomy above and <inline-formula><tex-math id=\"M15\">\\begin{document}$ d $\\end{document}<\/tex-math><\/inline-formula>-form functions with difference balanced property. Afterwards, three families of optimal constant composition codes from these partitioned difference families are obtained, and their parameters are also summarized.<\/p><\/jats:p>","DOI":"10.3934\/amc.2020120","type":"journal-article","created":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T11:46:30Z","timestamp":1610106390000},"page":"465","source":"Crossref","is-referenced-by-count":1,"title":["Three classes of partitioned difference families and their optimal constant composition codes"],"prefix":"10.3934","volume":"16","author":[{"given":"Shanding","family":"Xu","sequence":"first","affiliation":[{"name":"College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China"},{"name":"Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, China"}]},{"given":"Longjiang","family":"Qu","sequence":"additional","affiliation":[{"name":"College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Xiwang","family":"Cao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2020120-1","doi-asserted-by":"publisher","unstructured":"K. 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