From Linear Codes to Hyperplane Arrangements via Thomas Decomposition
Information Theory
2014-04-14 v2 math.IT
Abstract
We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight enumerator of a linear code. In particular, one can deal with infinitely many finite fields simultaneously by defining a weight enumerator for codes over infinite fields.
Cite
@article{arxiv.1202.3625,
title = {From Linear Codes to Hyperplane Arrangements via Thomas Decomposition},
author = {Wilhelm Plesken and Thomas Bächler},
journal= {arXiv preprint arXiv:1202.3625},
year = {2014}
}
Comments
This has been rejected since it contains some mistakes. A similar work has been publish in Documenta Math. vol. 19