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

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.

Keywords:

$G$-codes Finite chain rings, Formal power series rings, $\gamma$-adic codes,

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Journal of Algebra Combinatorics Discrete Structures and Applications-Cover

Başlangıç: 2015
Yayıncı: İrfan ŞİAP

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