Orthogonal designs and Type II codes over \(\mathbb Z_{2k}\)
The authors generalize known techniques using matrices to produce Type~I and Type~II codes over the ring \(\mathbb{Z}_{2k}.\) Type~II codes are self-dual codes such that all vectors have Euclidean weights congruent to 0 modulo \(4k\) and Type~I codes are self-dual codes that are not Type~II. They introduce two methods for constructing these codes using a generalization of orthogonal designs and compute several interesting examples of extremal codes. Type~II (resp. Type~I) real unimodular lattices are constructed from Type~II (resp. Type~I) codes, and several interesting examples of such lattices are also given.
scientific article; zbMATH DE number 1746298