Abstract
For a subspace arrangement over a finite field we study the evaluation code defined on the arrangements set of points. The length of this code is given by the subspace arrangements 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. A few examples are presented with high minimum distance and dimension.
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Acknowledgments
The authors are thankful to the Naval Academy and the Office of Naval Research for support through the Trident Scholar program. The authors would like to thank the reviewers for many excellent comments and suggestions that added depth and interest. The authors would also like to especially thank reviewer 2 for very efficiently streamlining the presentations and arguments of Lemma’s 2.5 and 2.6 and finding a gap in an earlier version of the proof of Theorem 1.12.
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Communicated by J. D. Key.
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Berg, J., Wakefield, M. Skeleton simplicial evaluation codes. Des. Codes Cryptogr. 72, 609–625 (2014). https://doi.org/10.1007/s10623-012-9793-0
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DOI: https://doi.org/10.1007/s10623-012-9793-0