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The $\\ell$- Galois LCD code is a linear code $C$ with $h_{\\ell}(C) = 0$. In this paper, we show that the dimension of the $\\ell$-Galois hull of a linear code is invariant under permutation equivalence and we provide a method to calculate the dimension of the $\\ell$-Galois hull by the generator matrix of the code. 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