On some classes of linear codes over $${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$$ Z 2 Z 4 and their covering radii

Abstract

In this paper, we define the simplex and MacDonald codes of types \(\alpha \) and \(\beta \) over \({\mathbb {Z}}_{2}{\mathbb {Z}}_{4}\). We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type \(\alpha \) meets the Gilbert bound.