Closest point algorithms with lp norm for root lattices

We study quantizers with l_p norm, with p ≥ 1, for the root lattices. Our algorithms extend the ones proposed by Conway and Sloane [1] with l₂ norm. They proposed an interesting algorithm for A_n lattice, but without proof of the optimality. We give the proof of the optimality with our extended case of l_p norm. We also give an algorithm for E₆ and its dual, which are not described in [1].