New metrics arising from matroids of linear codes

Abstract

In this paper, from each linear code in Fn q, we construct two metrics, the one called "the metric associated to it" and the other "the symmetrized metric associated to it." They are respectively defined in terms of the rank function and the rank and corank functions of the matroid of the linear code. Such metrics constructed from linear codes give rise to abundant new metrics on the space Fn q. We investigate their properties and illustrate our results with some examples.