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G-codes over Formal Power Series Rings and Finite Chain Rings
Dougherty, Steven Gildea, Joe Korban, Adrian
Dougherty, Steven
Gildea, Joe
Korban, Adrian
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2020-02-29
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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.
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Dougherty, 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.
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Journal of Algebra Combinatorics Discrete Structures and Applications
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https://doi.org/10.13069/jacodesmath.645026
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2148-838X