$G$-codes over formal power series rings and finite chain rings
DOI:
https://doi.org/10.13069/jacodesmath.645026Keywords:
$G$-codes, Finite chain rings, Formal power series rings, $\gamma$-adic codesAbstract
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.
Received: 17 May 2019 Accepted: 14 October 2019Downloads
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