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In this paper, we define the simplex and MacDonald codes of types $$\alpha $$ α and $$\beta $$ β over $${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$$ Z 2 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 $$\alpha $$ α meets the Gilbert bound.
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