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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2019 / Cilt: 9 - Sayı: 2

The Matrix Representation of A Rule of Cellular Automata and An Application to Coding Theory

Hücresel Dönüşümlerin Bir Kuralının Matris Temsili ve Kodlama Teorisinde Bir Uygulaması

Ferhat ŞAH
Pages
329–341
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

We gave an application of obtained block matrices to coding theory over the ternary field.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we studied the behavior of a family of three dimensional cellular automata under periodic boundary condition by using matrix algebra.
📊
Key Findings & Data:We obtained representation matrix of the this family with the help of polinomal algebra.
💡
Conclusion & Impact:We gave an application of obtained block matrices to coding theory over the ternary field.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we studied the behavior of a family of three dimensional cellular automata under periodic boundary condition by using matrix algebra. We obtained representation matrix of the this family with the help of polinomal algebra. We gave an application of obtained block matrices to coding theory over the ternary field.

Özet

Bu çalışmada, matris cebiri yardımıyla üç boyutlu bir hücresel dönüşüm ailesinin periyodik sınır şartı altında davranışını inceledik. Polinom cebiri yardımıyla bu ailenin temsil matrisini elde ettik. Elde edilen blok matrislerin üçlü cisimler üzerinde bir kodlama teorisi uygulamasını verdik.

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Cite This Article

ŞAH, F. (2022). The Matrix Representation of A Rule of Cellular Automata and An Application to Coding Theory. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 - Sayı: 2, 329–341. https://ajindex.com/articles/428487

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