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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 24 Sayı: 3

F_p R – Linear Skew Constacyclic Codes

F_p R – Lineer Çarpık Sabit Devirli Kodlar

Tülay Yıldırım(Karabük Üniversitesi)0000-0001-5933-9752
Pages
525–530
Publication Date
2024-06-27
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AI Summary & Key Takeaways

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

We also determine the generator polynomials and the Gray images of the skew constacyclic codes over the ring F_p R.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study a special class of linear codes, called skew constacyclic codes, over the ring F_p R, where R=F_p+vF_p, p is an odd prime number and v^2=v.
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Key Findings & Data:These codes are defined as a subset of the ring F_p^m R^n.
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Conclusion & Impact:We also determine the generator polynomials and the Gray images of the skew constacyclic codes over the ring F_p R.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Lineer kodlar · Skew polinom halkaları · Skew constacyclic kodlar

Abstract

In this paper, we study a special class of linear codes, called skew constacyclic codes, over the ring F_p R, where R=F_p+vF_p, p is an odd prime number and v^2=v. These codes are defined as a subset of the ring F_p^m R^n. For an automorphism θ of R, we investigate the structural properties of skew polynomial ring R[x,θ]. We also determine the generator polynomials and the Gray images of the skew constacyclic codes over the ring F_p R.

Özet

Bu makalede, 〖 F〗_p R halkası üzerinde skew constacyclic kodlar olarak adlandırılan özel bir doğrusal kod sınıfını olan çalışıyoruz, burada R=F_p+vF_p, p tek asal sayıdır ve v^2=v. Bu kodlar F_p^m R^n halkasının bir alt kümesi olarak tanımlanır. R nin bir θ otomorfizması için, R[x,θ] skew polinom halkasının yapısal özelliklerini araştırıyoruz. Ayrıca, F_p R halkası üzerinde skew constacyclic kodların üreteç polinomlarını ve Gray görüntülerini belirliyoruz.

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Cite This Article

Yıldırım, T. (2024). F_p R – Linear Skew Constacyclic Codes. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 24 Sayı: 3, 525–530. https://doi.org/10.35414/akufemubid.1331180

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