منابع مشابه
Toric complete intersection codes
In this paper we construct evaluation codes on zero-dimensional complete intersections in toric varieties and give lower bounds for their minimum distance. This generalizes the results of Gold–Little–Schenck and Ballico–Fontanari who considered evaluation codes on complete intersections in the projective space.
متن کاملOn dual toric complete intersection codes
In this paper we study duality for evaluation codes on intersections of d hypersurfaces with given d -dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of d = 2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and q...
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We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideal...
متن کاملOn the Geometry of Complete Intersection Toric Varieties
In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular, we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal to 2n − 2, is exac...
متن کاملToric residue codes: I
In this paper, we begin exploring the construction of algebraic codes from toric varieties using toric residues. Though algebraic codes have been constructed from toric varieties, they have all been evaluation codes, where one evaluates the sections of a line bundle at a collection of rational points. In the present paper, instead of evaluating sections of a line bundle at rational points, we c...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2013
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2012.08.006