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This article studies skew generalized quasi-cyclic codes (SGQC-codes) over finite fields for any length n. We derive generator polynomials and cardinality of SGQC codes. Moreover, we show that the dual of any length SGQC-code is also an SGQC-code. Our search results lead to the construction of fifteen new 2-generator SGQC codes over the finite field F 4 with minimum distances exceeding the minimum distances of the previously best known F 4 -linear codes with comparable parameters. [ABSTRACT FROM AUTHOR]