On the computation of coset leaders with high Hamming weight. (Q1421523)

In [IEEE Trans. Inf. Theory 43, 1820--1831 (1997; Zbl 0905.94035)], \textit{T. Helleseth} and \textit{T. Kløve} introduced the term `Newton radius' of a code as the largest weight of a uniquely correctable error. This paper gives an efficient algorithm for computing coset leaders of relatively high Hamming weight, using the modular representation of a linear code. The weights of these coset leaders serve as lower bounds on the Newton radius and the covering radius for linear codes. Using the algorithm presented in this paper, the author is also able to improve some of the lower bounds for the Newton radius for binary first-order Reed-Muller codes.