Special subsets and optimum codes based on lattices and cosets

This paper introduces the concept of special subsets (Farrell et al. 1987) when applied to generator matrices based on lattices and cosets as presented by Calderbank and Sloane (1987). By using the special subsets we propose a non-exhaustive code search for optimum codes. Although non-exhaustive, the search always results in optimum codes for given (k₁,V,Λ/Λ´). Tables with binary and ternary optimum codes to partitions of lattices with 8, 9 and 16 cosets, were obtained