Hücresel Dönüşümlerin Bir Kuralının Matris Temsili ve Kodlama Teorisinde Bir Uygulaması

Yıl 2019, Cilt: 9 Sayı: 2, 329 - 341, 30.12.2019

Ferhat Şah

https://doi.org/10.37094/adyujsci.551180

Öz

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.

Anahtar Kelimeler

Üç boyutlu hücresel dönüşüm, Kural matris, Hata düzelten kodlar

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

Öz

 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.

 

Anahtar Kelimeler

Three Dimensional Cellular Automata, Rule Matrix, Error Correcting Codes

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