{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:12:31Z","timestamp":1760710351343},"reference-count":18,"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":"<p style='text-indent:20px;'>Combinatorial <inline-formula><tex-math id=\"M1\">\\begin{document}$ t $\\end{document}<\/tex-math><\/inline-formula>-designs have been an interesting topic in combinatorics for decades. It is a basic fact that the codewords of a fixed weight in a code may hold a <inline-formula><tex-math id=\"M2\">\\begin{document}$ t $\\end{document}<\/tex-math><\/inline-formula>-design. Till now only a small amount of work on constructing <inline-formula><tex-math id=\"M3\">\\begin{document}$ t $\\end{document}<\/tex-math><\/inline-formula>-designs from codes has been done. In this paper, we determine the weight distributions of two classes of cyclic codes: one related to the triple-error correcting binary BCH codes, and the other related to the cyclic codes with parameters satisfying the generalized Kasami case, respectively. We then obtain infinite families of <inline-formula><tex-math id=\"M4\">\\begin{document}$ 2 $\\end{document}<\/tex-math><\/inline-formula>-designs from these codes by proving that they are both affine-invariant codes, and explicitly determine their parameters. In particular, the codes derived from the dual of binary BCH codes hold five <inline-formula><tex-math id=\"M5\">\\begin{document}$ 3 $\\end{document}<\/tex-math><\/inline-formula>-designs when <inline-formula><tex-math id=\"M6\">\\begin{document}$ m = 4 $\\end{document}<\/tex-math><\/inline-formula>.<\/p><\/jats:p>","DOI":"10.3934\/amc.2020106","type":"journal-article","created":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T08:48:15Z","timestamp":1598258895000},"page":"157","source":"Crossref","is-referenced-by-count":10,"title":["Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros"],"prefix":"10.3934","volume":"16","author":[{"given":"Xiaoni","family":"Du","sequence":"first","affiliation":[]},{"given":"Rong","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Chunming","family":"Tang","sequence":"additional","affiliation":[]},{"given":"Qi","family":"Wang","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2020106-1","doi-asserted-by":"publisher","unstructured":"E. 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