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This paper presents two complementary constructions of finite-length non-binary protograph-based codes with the focus on the short block-length regime. The first class is based on the existing approaches of applying the copy-and-permute operations to the constituent protograph with unweighted edges, followed by assigning non-binary scales to the edges of the derived graph. The second class is novel and is based on the so-called graph cover of a non-binary protograph: the original protograph has fixed edge scalings and copy-and-permute operations are applied to the edge-weighted protograph. The second class is arguably more restrictive, but in turn it offers simpler design and implementation. We provide design and construction of these non-binary codes for short block-lengths. Performance, cycle distribution and the minimum distance of the binary image of selected codes over AWGN is provided for information block-lengths as low as 64 bits.