From Linear Codes to Hyperplane Arrangements via Thomas Decomposition
- Resource Type
- Working Paper
- Authors
- Plesken, Wilhelm; Bächler, Thomas
- Source
- Subject
- Computer Science - Information Theory
- Language
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.
Comment: This has been rejected since it contains some mistakes. A similar work has been publish in Documenta Math. vol. 19