Skeleton Simplicial Evaluation Codes

Abstract

For a subspace arrangement over a finite field we study the evaluation code defined on the arrangement's set of points. The length of this code is given by the subspace arrangement's characteristic polynomial. For coordinate subspace arrangements, the dimension is bounded below by the face vector of the corresponding simplicial complex. The minimum distance is determined for coordinate subspace arrangements where the simplicial complex is a skeleton.

16 pages, 2 figures