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Inspired by the works \\cite{Li-Zeng-Hu} and \\cite{gegeng2}, we study two families of cyclic codes over $\\mathbb{F}_p$ with arbitrary number of zeroes of generalized Niho type, more precisely $\\ca$ (for $p=2$) of $t+1$ zeroes, and $\\cb$ (for any prime $p$) of $t$ zeroes for any $t$. 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