G-codes over formal power series rings and finite chain rings.

In this work, we define G-codes over the infinite ring R_∞ as ideals in the group ring R_∞G. We show that the dual of a G-code is again a G-code in this setting. We study the projections and lifts of G-codes over the finite chain rings and over the formal power series rings respectively. We extend known results of constructing -adic codes over R_∞ to γ-adic G-codes over the same ring. We also study G-codes over principal ideal rings. [ABSTRACT FROM AUTHOR]