@article{article_645026, title={$G$-codes over formal power series rings and finite chain rings}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={7}, pages={55–71}, year={2020}, DOI={10.13069/jacodesmath.645026}, author={Dougherty, Steven T. and Gildea, Joe and Korban, Adrian}, keywords={$G$-codes,Finite chain rings,Formal power series rings,$\gamma$-adic codes}, abstract={In 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.}, number={1}, publisher={iPeak Academy}