Self-dual codes over finite chain rings

Self-dual codes are an important class of codes. They have interesting connections to design theory, lattices theory and invariant theory. In this work, we generalize our result of [15] to finite chain rings R, and define Type II codes over finite chain rings R. A new Gray map between codes over finite chain rings R and codes over F₂ is defined. Properties of the Gray map which take self-dual codes over finite chain rings R to self-dual codes over F₂ are studied.