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For any integral convex polytope in R 2 there is an explicit construction of an error-correcting code of length (q − 1) 2 over the finite field F q , obtained by evaluation of rational functions on a toric surface associated to the polytope. The dimension of the code is equal to the number of integral points in the given polytope and the minimum distance is(More)
Foundation 1 Abstract We consider dynamic evaluation of algebraic functions (matrix mul-) is an algebraic problem, we consider serving on-line requests of the form " change input x i to value v " or " what is the value of output y i ? ". We present techniques for showing lower bounds on the worst case time complexity per operation for such problems. The(More)
We study subsets of Grassmann varieties G(l, m) over a field F , such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study the linear spans of, and in case of positive characteristic, the number of Fq-rational points on such unions. Moreover we study a geometric duality of such unions, and give a combinatorial(More)