Cyclic codes over Z4+uZ4+u2Z4Z4+uZ4+u2Z4\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}

Mehmet ÖZEN; Nazmiye Tuğba ÖZZAİM; Nuh AYDIN

Makale detayları

Cyclic codes over Z4+uZ4+u2Z4Z4+uZ4+u2Z4\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}

Yazarlar:

Mehmet ÖZEN | Nazmiye Tuğba ÖZZAİM | Nuh AYDIN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2017 Vol.41 Issue 5, pp.1235-1247

Belge Tipi:

Makale

Yayın Tarihi:

9/2017

Belge Dili:

Türkçe

Document ID (Org No.):

2000745999

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this paper, we study cyclic codes over the ring R=Z4+uZ4+u2Z4R=Z4+uZ4+u2Z4R=\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4},where u3=0u3=0u^{3}=0. We investigate Galois extensions of this ring and the ideal structure of these extensions.The results are then used to obtain facts about cyclic codes over RRR. We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over Z4Z4\mathbb{Z}_4 by considering Gray images of cyclic codes over RRR.

Makale detayları

Cyclic codes over Z4+uZ4+u2Z4Z4+uZ4+u2Z4\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}

Yazarlar: Mehmet ÖZEN | Nazmiye Tuğba ÖZZAİM | Nuh AYDIN

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2017 Vol.41 Issue 5, pp.1235-1247

Belge Tipi: Makale

Yayın Tarihi: 9/2017

Belge Dili: Türkçe

Document ID (Org No.): 2000745999

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Mehmet ÖZEN | Nazmiye Tuğba ÖZZAİM | Nuh AYDIN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2017 Vol.41 Issue 5, pp.1235-1247

Belge Tipi:

Makale

Yayın Tarihi:

9/2017

Belge Dili:

Türkçe

Document ID (Org No.):

2000745999

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098