In this paper we use the Gröbner representation of a binary linear code [Formula: see text] to give efficient algorithms for computing the whole set of coset leaders, denoted by [Formula: see text] and the set of leader codewords, denoted by [Formula: see text]. The first algorithm could be adapted to provide not only the Newton and the covering radius of [Formula: see text] but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation established between zero neighbors and leader codewords.
No Projective 16-Divisible Binary Linear Code of Length 131 Exists
