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The construction and counting with regard to orthomorphic permutations (also known as orthomorphism) over a general Galois field is one of the problems with widely applied and common research in the field of cryptography design and analysis. The orthomorphism emerged in a polynomial form involving the general p – characteristic Galois field is a critical crucial way to in-depth and long-term research. And this paper is encompassing the coefficients constraint relation concerning orthomorphic polynomials form over the general Galois field by algebraic way. On the other side of the coin, the authors talk about the structure and counting problems with regard to maximal subgroups in a finite commutative group. It is useful for me to have a further study about the application and nature of the theory relating to the orthomorphism polynomial.