Minimum Degree-Weighted Distance Decoding for Polynomial Residue Codes with Non-Coprime Moduli

This letter presents a new decoding algorithm called the minimum degree-weighted distance decoding for polynomial residue codes with non-coprime moduli. The newly proposed decoding is based on the degree-weighted distance and is different from the traditional minimum Hamming distance decoding. It is shown that for the two types of minimum distance decoders, i.e., the minimum degree-weighted distance decoding and the minimum Hamming distance decoding, one is not absolutely stronger than the other, but they can complement each other from different points of view.