A DETAILED STUDY OF THE RELATIONSHIP BETWEEN SOME OF THE ROOT LATTICES AND THE CODING THEORY
Michio Ozeki · Kyushu Journal of Mathematics · 2018
In the present article we study the even unimodular lattice which lies between the root lattice m · An and the dual lattice (m · An)#. Here m · An is an orthogonal sum of m copies of the root lattice An. In the course of the study the code over the ring A#n/ An arises in a natural way. We find that an intimate relationship between the even unimodular lattice containing m · An as a sublattice and the error correcting code over the ring A#n/ An exists. As a consequence we could reconstruct sixteen non-isometric Niemeier lattices out of twenty-four non-isometric lattices by using the present approach.