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Discussion Paper

The Generalized Basis Reduction Algorithm

Let F(x) be a convex function defined in Rn, which is symmetric about the origin and homogeneous of degree 1, and let L be the lattice of integers Zn. A definition of a reduced basis, b1, …, bn, of the lattice with respect to the distance function F is presented, and we describe an algorithm which yields a reduced basis in polynomial time, for fixed n.