Flags and Lattice Basis Reduction

In this lecture we give a self-contained introduction to the theory of lattices in Euclidean vector spaces. We reinterpret a large class of lattice basis reduction algorithms by using the concept of a "flag". In our reformu- lation, lattice basis reduction algorithms are more appropriately called "flag reduction" algorithms. We address a problem that arises when one attempts to find a particularly good flag for a given lattice.