Bounds on the Minimum Homogeneous Distance of the pr-ary Image of Linear Block Codes over the Galois Ring GR(pr, m)

In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(p^r ,m), with respect to any basis of GR(p^r, m). These bounds depend on the parameters of GR(p^r , m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Z_pr. Examples are given of Galois ring codes that meet these bounds.