The invariant theory of finite groups can connect the coding theory to the number theory. In this paper, under this conformity, we obtain the minimal generators of the rings of E-polynomials constructed from the groups related to $\mathbb{Z}_4$-codes. In addition, we determine the generators of the invariant rings appearing by E-Polynomials and complete weight enumerators of Type II $\mathbb{Z}_4$-codes.

Let $C^1([0,1], A)$ be the Banach algebra of all continuously differentiable maps from the closed unit interval $[0,1]$ to a uniform algebra $A$ with respect to certain norms. We prove that every surjective, not necessarily linear, isometry on $C^1([0,1], A)$ is represented by homeomorphisms on $[0,1]$ and the maximal ideal space of $A$.