Mathematics – Algebraic Geometry
Scientific paper
2008-11-17
Journal of Symbolic Computation 45 (2010) 734
Mathematics
Algebraic Geometry
30 pages, 9 figures; v2: replaced fansy cycles with fansy divisors
Scientific paper
10.1016/j.jsc.2010.03.008
A description of complete normal varieties with lower dimensional torus action has been given by Altmann, Hausen, and Suess, generalizing the theory of toric varieties. Considering the case where the acting torus T has codimension one, we describe T-invariant Weil and Cartier divisors and provide formulae for calculating global sections, intersection numbers, and Euler characteristics. As an application, we use divisors on these so-called T-varieties to define new evaluation codes called T-codes. We find estimates on their minimum distance using intersection theory. This generalizes the theory of toric codes and combines it with AG codes on curves. As the simplest application of our general techniques we look at codes on ruled surfaces coming from decomposable vector bundles. Already this construction gives codes that are better than the related product code. Further examples show that we can improve these codes by constructing more sophisticated T-varieties. These results suggest to look further for good codes on T-varieties.
Ilten Nathan
Süß Hendrik
No associations
LandOfFree
AG Codes from Polyhedral Divisors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with AG Codes from Polyhedral Divisors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and AG Codes from Polyhedral Divisors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-466783