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In this paper, we show that if $q^e|d$, then $C$ has a basis consisting of $k$ codewords such that the first $\\min\\left\\{e+1,k\\right\\}$ of them span a Griesmer subcode with constant weight $d$ and any $k-1$ of them span a $[g_q(k-1,d),k-1,d]_q$ Griesmer subcode. 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