Bounds on the Minimum Homogeneous Distance of the ${p^{r}}$-ary Image of Linear Block Codes Over the Galois Ring ${hbox{GR}}(p^{r},m)$

摘要

In this correspondence, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(pr,m), with respect to any basis of GR(pr,m). These bounds depend on the parameters of GR(pr ,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