A Class of Skew-Cyclic Codes over (Z_(2^m ) [u])/〈u^2-r〉    with Derivation

Hayrullah Özimamoğlu

Makale detayları

A Class of Skew-Cyclic Codes over (Z_(2^m ) [u])/〈u^2-r〉 with Derivation

Yazarlar:

Hayrullah Özimamoğlu

Yayıncı:

Erzincan Binali Yildirim University

Ana Başlıklar:

Mühendislik

Dergi:

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.16 Issue 2, pp.327-344

Belge Tipi:

Makale

Yayın Tarihi:

8/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001294144

pISSN:

2149-4584

Anahtar kelimeler:

Özet:

 Let R_rZ_2m uZ_2m  be a finite ring, where u2r for rZ_2m , m is a positive integer, and m2. In this paper, we study a class of skew-cyclic codes using a skew polynomial ring over R_r with an automorphism θ_r and a derivation δ_θ_r . We generalize the skew-cyclic codes over Z_4uZ_4; u21 to the skew-cyclic codes over R_r, and call such codes as δ_θ_r -cyclic codes. We investigate the structures of a skew polynomial ring R_r x,θ_r,δ_θ_r  . A δ_θ_r -cyclic code is showed to be a left R_r x,θ_r,δ_θ_r  -submodule of R_r x,θ_r,δ_θ_r  xn-1 . We give the generator matrix of a δ_θ_r -cyclic code of length n over R_r. Also, we present the generator matrix of the dual of a free δ_θ_r -cyclic code of even length n over R_r.

 Let R_rZ_2m uZ_2m  be a finite ring, where u2r for rZ_2m , m is a positive integer, and m2. In this paper, we study a class of skew-cyclic codes using a skew polynomial ring over R_r with an automorphism θ_r and a derivation δ_θ_r . We generalize the skew-cyclic codes over Z_4uZ_4; u21 to the skew-cyclic codes over R_r, and call such codes as δ_θ_r -cyclic codes. We investigate the structures of a skew polynomial ring R_r x,θ_r,δ_θ_r  . A δ_θ_r -cyclic code is showed to be a left R_r x,θ_r,δ_θ_r  -submodule of R_r x,θ_r,δ_θ_r  xn-1 . We give the generator matrix of a δ_θ_r -cyclic code of length n over R_r. Also, we present the generator matrix of the dual of a free δ_θ_r -cyclic code of even length n over R_r.

 Let R_rZ_2m uZ_2m  be a finite ring, where u2r for rZ_2m , m is a positive integer, and m2. In this paper, we study a class of skew-cyclic codes using a skew polynomial ring over R_r with an automorphism θ_r and a derivation δ_θ_r . We generalize the skew-cyclic codes over Z_4uZ_4; u21 to the skew-cyclic codes over R_r, and call such codes as δ_θ_r -cyclic codes. We investigate the structures of a skew polynomial ring R_r x,θ_r,δ_θ_r  . A δ_θ_r -cyclic code is showed to be a left R_r x,θ_r,δ_θ_r  -submodule of R_r x,θ_r,δ_θ_r  xn-1 . We give the generator matrix of a δ_θ_r -cyclic code of length n over R_r. Also, we present the generator matrix of the dual of a free δ_θ_r -cyclic code of even length n over R_r.

 Let R_rZ_2m uZ_2m  be a finite ring, where u2r for rZ_2m , m is a positive integer, and m2. In this paper, we study a class of skew-cyclic codes using a skew polynomial ring over R_r with an automorphism θ_r and a derivation δ_θ_r . We generalize the skew-cyclic codes over Z_4uZ_4; u21 to the skew-cyclic codes over R_r, and call such codes as δ_θ_r -cyclic codes. We investigate the structures of a skew polynomial ring R_r x,θ_r,δ_θ_r  . A δ_θ_r -cyclic code is showed to be a left R_r x,θ_r,δ_θ_r  -submodule of R_r x,θ_r,δ_θ_r  xn-1 . We give the generator matrix of a δ_θ_r -cyclic code of length n over R_r. Also, we present the generator matrix of the dual of a free δ_θ_r -cyclic code of even length n over R_r.

Makale detayları

A Class of Skew-Cyclic Codes over (Z_(2^m ) [u])/〈u^2-r〉 with Derivation

Yazarlar:

Hayrullah Özimamoğlu

Yayıncı:

Erzincan Binali Yildirim University

Ana Başlıklar:

Mühendislik

Dergi:

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.16 Issue 2, pp.327-344

Belge Tipi:

Makale

Yayın Tarihi:

8/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001294144

pISSN:

2149-4584

cyclic codes

skew polynomial rings

skew-cyclic codes

Sayı

Makale detayları

A Class of Skew-Cyclic Codes over (Z_(2^m ) [u])/〈u^2-r〉 with Derivation

Yazarlar: Hayrullah Özimamoğlu

Yayıncı: Erzincan Binali Yildirim University

Ana Başlıklar: Mühendislik

Dergi: Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.16 Issue 2, pp.327-344

Belge Tipi: Makale

Yayın Tarihi: 8/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001294144

pISSN: 2149-4584

cyclic codes

skew polynomial rings

skew-cyclic codes

Sayı

Yazarlar:

Hayrullah Özimamoğlu

Yayıncı:

Erzincan Binali Yildirim University

Ana Başlıklar:

Mühendislik

Dergi:

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.16 Issue 2, pp.327-344

Belge Tipi:

Makale

Yayın Tarihi:

8/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001294144

pISSN:

2149-4584