On Octonary Codes and their Covering Radii

This paper introduces new reduction and torsion codes for an octonary code and determines their basic properties. These could be useful for the classification of self-orthogonal and self dual codes over $\mathbb{Z}_8$. We also focus our attention on covering radius problem of octonary codes. In particular, we determine lower and upper bounds of the covering radius of several classes of Repetition codes, Simplex codes of Type $\alpha$ and Type $\beta$ and their duals, MacDonald codes, and Reed-Muller codes over $\mathbb{Z}_8$.