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Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2026 / Cilt: 7 Sayı: 1 Özel Sayı

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

Steven T. Dougherty0000-0003-4877-1923
Joe Gildea0000-0001-7242-779X
Adrian Korban0000-0001-5206-6480
Pages
55–71
Publication Date
2020-02-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also study $G$-codes over principal ideal rings.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we define $G$-codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\infty G$.
📊
Key Findings & Data:We show that the dual of a $G$-code is again a $G$-code in this setting.
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Conclusion & Impact:We also study $G$-codes over principal ideal rings.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:$G$-codes · Finite chain rings · Formal power series rings

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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Cite This Article

Dougherty, S. T., Gildea, J., Korban, A. (2020). $G$-codes over formal power series rings and finite chain rings. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 7 Sayı: 1 Özel Sayı, 55–71. https://doi.org/10.13069/jacodesmath.645026

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