Msri-up 2009 Project Topic Ideas
نویسندگان
چکیده
General Background. In [6], [7], J. Hansen introduced these codes using some constructions from algebraic geometry (toric varieties). In somewhat more downto-earth language than he used, let P ⊂ R be an integral convex polytope (the convex hull of some set of integer lattice points). (The book [18] as a good general reference for the geometry of polytopes.) Suppose that P∩Zm is properly contained in the rectangular box [0, q−2]m (which we denote ¤q−1), for some prime power q. Then a toric code is obtained by evaluating linear combinations of the monomials with exponent vector in P ∩Zm at some subset (usually all) of the points of (F ∗ q ). We formalize this in the following definition.
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