From Linear Codes to Hyperplane Arrangements via Thomas Decomposition
  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. 
Wilhelm Plesken, Thomas B\"achler
cs.IT math.IT