On construction D and related constructions of lattices from linear codes
Date of Issue2013
International Workshop on Coding and Cryptography (2013 : Bergen, Norway)
School of Physical and Mathematical Sciences
We investigate three closely related constructions of lattices from linear codes: the classical Construction D, Construction D ̅, and the recently developed Construction A’. These constructions have been proven useful and result in efficient encoding and decoding algorithms for Barnes-Wall lattices. Here we analyze their applications in a general setting. We show that Construction D ̅ produces a lattice packing if and only if the nested codes being used are closed under Schur product, thus proving the similarity of Construction D and Construction D ̅ when applied to Reed-Muller codes. In addition, we provide a correspondence between nested binary linear codes and codes over polynomial rings. This proves that Construction A’ does not always produce a lattice, but any lattices constructible using Construction D ̅ are also constructible using Construction A’. This result also gives a partial condition for Construction A’ to produce a lattice.
DRNTU::Engineering::Civil engineering::Construction technology
© 2013 The International Workshop on Coding and Cryptography(WCC 13).