This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive $[n,3.5,n-t]_4$ codes for all $t$ with variable $n$, except for $t=6,7,12$.

翻译：本文旨在构造具有非整数维度的最优四元加法码。首先，我们提出了四元加法等重码的组合构造方法，以及加法反码构造。随后，我们提出了广义的构造X，它有助于从线性码构造非整数维度的最优加法码。接着，我们通过这两种方法构造了十类最优四元非整数维度加法码。作为应用，我们还确定了所有$t$（除$t=6,7,12$外）对应可变$n$的最优加法$[n,3.5,n-t]_4$码。