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In this paper, by using a relation between binomial ideal and submodules of Z ⁿ in , a submodule associated with the integer programming (IP) problem is defined. By computing the reduced Gröbner basis (RGB) of the submodule, the decoding problem of non-binary q-ary codes is considered as an integer program problem. Decoding complexity is investigated and the effective factors in complexity are also determined. Furthermore, an example of the decoding method for a 3-ary code is provided.