Computing coset leaders and leader codewords of binary codes

In this paper we use the Grobner representation of a binary linear code to give efficient algorithms for computing the whole set of coset leaders, denoted by and the set of leader codewords, denoted by . The first algorithm could be adapted to provide not only the Newton and the covering radius of 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.

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