Dougherty, StevenGildea, JoeKorban, Adrian2019-10-162019-10-162020-02-29Dougherty, S., Gildea, J. & Korban, A. (2020). G-codes over Formal Power Series Rings and Finite Chain Rings. Journal of Algebra Combinatorics Discrete Structures and Applications, 7(1), 55-71.https://doi.org/10.13069/jacodesmath.645026http://hdl.handle.net/10034/622726In this work, we define $G$-codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\infty G$. 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 $\gamma$-adic codes over $R_\infty$ to $\gamma$-adic $G$-codes over the same ring. We also study $G$-codes over principal ideal rings.https://creativecommons.org/licenses/by/4.0/$G$-codesFinite chain ringsFormal power series rings$\gamma$-adic codesArticle2148-838XJournal of Algebra Combinatorics Discrete Structures and Applications