9 research outputs found
Computing coset leaders and leader codewords of binary codes
In this paper we use the Gr\"obner 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 stablished
between zero neighbours and leader codewords
Improved evaluation codes defined by plane valuations
We study improved evaluation codes associated with finitely generated order structures given by plane valuations. We show minimal sets of generators of the semigroups of these structures and provide parameters for the corresponding improved evaluation codes. © 2010 Elsevier Inc. All rights reserved