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

## TL;DR

This paper introduces a novel decoding method for polynomial residue codes called minimum degree-weighted distance decoding, which offers a different perspective from traditional Hamming distance decoding and can complement it.

## Contribution

The paper proposes a new decoding approach based on degree-weighted distance for polynomial residue codes, expanding the decoding strategies beyond traditional methods.

## Key findings

- The new decoding method is based on degree-weighted distance.
- It is shown that the new and traditional decoders can complement each other.
- Neither decoder is strictly stronger than the other.

## Abstract

This paper presents a new decoding for polynomial residue codes, called the minimum degree-weighted distance decoding. The newly proposed decoding is based on the degree-weighted distance and 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.