Systematic Encoding and Permutation Decoding for Z_p^s-Linear Codes

Linear codes over Z ps of length n are subgroups of Z psn. These codes are also called Z ps-additive codes and can be seen as a generalization of linear codes over Z 2} and Z 4}. A Z ps-linear code is a code over Z p} , not necessarily linear, which is the generalized Gray map image of a Z ps-additive code. In 2015, a systematic encoding was found for Z 4} -linear codes. Moreover, an alternative permutation decoding method, which is suitable for any binary code (not necessarily linear) with a systematic encoding, was established. In this paper, we generalize these results by presenting a systematic encoding for any Z ps-linear code with s≥q 2 and p prime. We also describe a permutation decoding method for any systematic code over Z p} , not necessarily linear, and show some examples of how to use this systematic encoding in this decoding method.