Preparata codes through lattices
We define an elementary family of lattices, from which we obtain a family of extended cyclic codes with coefficients in the modular integers. The first nontrivial subfamily is the family of quaternary Preparata codes. The family of dual codes coincides with the extended low-correlation sequences introduced by Kumar, Helleseth, and Calderbank.
preparata code lattice cyclic code goethals code modular code