On the covering dimension of a linear code
Information Theory
2015-04-10 v1 math.IT
Abstract
The critical exponent of a matroid is one of the important parameters in matroid theory and is related to the Rota and Crapo's Critical Problem. This paper introduces the covering dimension of a linear code over a finite field, which is analogous to the critical exponent of a representable matroid. An upper bound on the covering dimension is conjectured and nearly proven, improving a classical bound for the critical exponent. Finally, a construction is given of linear codes that attain equality in the covering dimension bound.
Keywords
Cite
@article{arxiv.1504.02357,
title = {On the covering dimension of a linear code},
author = {Thomas Britz and Keisuke Shiromoto},
journal= {arXiv preprint arXiv:1504.02357},
year = {2015}
}