Bounds on the Minimum Homogeneous Distance of the p@@ur@-ary Image of Linear Block Codes Over the Galois Ring GR(p@@ur@,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@@ur@,m), with respect to any basis of GR(p@@ur@,m). These bounds depend on the parameters of GR(p@@ur @,m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zopf @@dp@ @@ur@. Examples are given of Galois ring codes that meet these bounds.