F_p R – Linear Skew Constacyclic Codes

Year 2024, , 525 - 530, 27.06.2024

Tülay Yıldırım

https://doi.org/10.35414/akufemubid.1331180

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.

Keywords

Linear codes, Skew polynomial rings, Skew constacyclic codes;, Skew cyclic codes

F_p R – Lineer Çarpık Sabit Devirli Kodlar

Abstract

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.

Keywords

Lineer kodlar, Skew polinom halkaları, Skew constacyclic kodlar, Skew devirli kodlar

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