Construction of reversible integer codes with large moduli via Chinese remainder theorem

The codes over rational integer residue rings are called integer codes. In this paper, we give a necessary and sufficient condition concerning the generator matrices when integer codes are to be reversible and show that their reversibility is preserved from the decomposition of integer codes by Chinese remainder theorem. This brings an efficient method for constructing of reversible integer codes with large moduli. Using this method, we enumerate reversible self-dual integer codes of length 3,4 with various moduli. Further, we claim that reversible and self-dual integer codes produce reversible and unimodular lattices, respectively. As a result, we see that the extended binary Hamming code produces the even unimodular lattice of rank 8 and in particular this lattice is reversible, and furthermore the lattice induces an extremal Type II integer code of length 8 with modulus 4.