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

In this correspondence, 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 Zopf _p ^r. Examples are given of Galois ring codes that meet these bounds