Abstract

The orthomorphism on the Galois field is a kind of permutations that is the most widely used in cross-cutting issue, the orthomorphic polynomials over the finite field is an effective method to study it, this study has obtained the coefficients relationship of the orthomorphisms over the Galois field by algebraic methods. In addition, this study have understood the maximal subgroup structure and counting in the Abelian group. It is help to in-depth study the application and the nature of the orthomorphism qua the theoretical support.

Keywords:

Orthomorphic polynomials, orthomorphisms, the domain of algebraic integer, the finite field, the maximal subgroup,

References

Competing interests

The authors have no competing interests.

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The authors have no competing interests.