On One-Weight and ACD Codes in $\mathbb{Z}^{r}_{2}\times\mathbb{Z}^{s}_{4}\times\mathbb{Z}^{t}_{8}$

Abstract

In this paper, one-weight and additive complementary dual (ACD) codes in $\mathbb{Z}^{r}_{2}\times\mathbb{Z}^{s}_{4}\times\mathbb{Z}^{t}_{8}$ are studied. Firstly, it is shown that the image of an
equidistant $\mathbb{Z}_{2}\mathbb{Z}_{4}\mathbb{Z}_{8}$-additive code is a binary equidistant code. Then, some properties of the
structure and possible weights for one-weight $\mathbb{Z}_{2}\mathbb{Z}_{4}\mathbb{Z}_{8}$-additive codes are described.
Finally, it is given the sufficient conditions for a $\mathbb{Z}_{2}\mathbb{Z}_{4}\mathbb{Z}_{8}$-additive code to be ACD.