On the covering dimension of a linear code

Thomas Britz; Keisuke Shiromoto

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arXiv · 1504.02357

On the covering dimension of a linear code

Thomas Britz·Keisuke Shiromoto

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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.

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Thomas Britz, Keisuke Shiromoto. 2015-04-09. On the covering dimension of a linear code. https://arxiv.org/abs/1504.02357

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