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In this paper, we introduce a general construction of linear codes with smalldimension hull from any non LCD codes. Furthermore, we show that for any linearcode $\Co$ over $\F_q$ ($q > 3$) with $dim(Hull(\Co))=h$ there exist anequivalent codes $\Co_j$ with $dim(Hull(\Co_j))=j$ for any integer $0\leq j\leq h$. We also introduce the notion of pure LCD code; an LCD code and all itsequivalent are LCD; and construct an infinite family of pure LCD codes. Inaddition, we introduce a general construction of linear codes with onedimension hull.

Linear codes with arbitrary dimensional hull and pure LCD code