On the computation of coset leaders with high Hamming weight

The Newton radius of a code is the largest weight of a uniquely correctable error. The covering radius is the largest distance between a vector and the code. In this paper, we use the modular representation of a linear code to give an efficient algorithm for computing coset leaders of relatively high Hamming weight. The weights of these coset leaders serve as lower bounds on the Newton radius and the covering radius for linear codes.