From Linear Codes to Hyperplane Arrangements via Thomas Decomposition
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1202.3625 شماره
صفحات -
تاریخ انتشار 2012