On construction of Barnes-Wall lattices

Abstract

This paper presents the construction for decomposable Barnes-Wall principal sublattices (BWPSL) especially in rotated version, based on augmenting the product lattices involving lower dimensional component lattices from the same family. Particularly, a product lattice is constructed for which no additional augmenting is required. Certain properties of parameters including minimum distance and coding gain of augmented lattice are derived with a few examples.