Abstract: In this study, the Gröbner bases of modules are employed as a tool to analyze block length of RS code. A coordinate permutation of a RS code, which is defined over GF(pm) in GF(p), the polynomial vector form of the result can be considered as a sub module. Based on the algebraic structure of quasi-cyclic codes, the Gröbner bases of such a sub-module shed light on block length and dimension of the original code. Thus, block length of the code can be estimated. Furthermore, the primitive polynomial and generator polynomial of the code are reconstructed through Galois Field Fourier Transform (GFFT) technique.