Konferans Bildirisi

Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$

Cilt: 3 Sayı: 1 15 Aralık 2020
Conference Proceedings of Science and Technology Kapak
Conference Proceedings of Science and Technology
PDF İndir
EN

Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$

Abstract

In this paper, we introduce the ring $R=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ where $u^{2}=u$, $v^{2}=v$, $uv=vu=0$ over which the linear codes are studied. it's shown that the ring $R=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ is a commutative, characteristic 8 ring with $u^{2}=u$, $v^{2}=v$, $uv=vu=0$. Also, the ideals of $\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ are found. Moreover, we define the Lee distance and the Lee weight of an element of $R$ and investigate the generator matrices of the linear code and its dual.

Keywords

Kaynakça

  1. 1 A.R. Hammons, V. Kumar, A.R. Calderbank, N.J.A. Sloane, P. Solé, The Z4 -linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), 301-319.
  2. 2 S.T.Dougherty, P. Gaborit, M. Harada, P.Solé, Type II codes over F2 + uF2, IEEE Trans. Inf. Theory 45 (1999), 32–45.
  3. 3 B. Yildiz and S. Karadeniz, Linear Codes over Z4 + uZ4: MacWilliams Identities Projections, and Formally Self-Dual Codes, Finite Fields and Their Applications, 27 (2014), 24–40.
  4. 4 V. Sison and M. Remillion, Isometries and binary images of linear block codes over Z4 + uZ4 and Z8 + uZ8, The Asian Mathematical Conference (AMC 2016), (2016), 313-318.
  5. 5 A. Dertli and Y. Cengellenmis, On the Codes Over the Ring Z4 + uZ4 + vZ4 Cyclic, Constacyclic, Quasi-Cyclic Codes, Their Skew Codes, Cyclic DNA and Skew Cyclic DNA Codes, Prespacetime Journal, 10(2) (2019), 196-213.
  6. 6 S.T. Dougherty T. A. Gulliver, J. Wong, Self-dual codes over Z8 and Z9, Designs, Codes and Cryptography, 41 (2006), 235-249.
  7. 7 P. Li, X. Guo, S. Zhu, Some results of linear codes over the ring Z4 + uZ4 + vZ4 + uvZ4, Journal of Applied Mathematics and Computing, 54 (2017), 307–324.
  8. 8 J. Wood, Duality for modules over finite rings and applications to coding theory, Am. J. Math., 121(3) (1999), 555–575.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Konferans Bildirisi

Yazarlar

Yayımlanma Tarihi

15 Aralık 2020

Gönderilme Tarihi

2 Temmuz 2020

Kabul Tarihi

26 Eylül 2020

Yayımlandığı Sayı

Yıl 2020 Cilt: 3 Sayı: 1

IZ

https://izlik.org/JA69XL87NF

Kaynak Göster

RIS / Bibtex
APA
Çalışkan, B. (2020). Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology, 3(1), 19-23. https://izlik.org/JA69XL87NF
AMA
1.Çalışkan B. Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology. 2020;3(1):19-23. https://izlik.org/JA69XL87NF
Chicago
Çalışkan, Basri. 2020. “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”. Conference Proceedings of Science and Technology 3 (1): 19-23. https://izlik.org/JA69XL87NF.
EndNote
Çalışkan B (01 Aralık 2020) Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology 3 1 19–23.
IEEE
[1]B. Çalışkan, “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”, Conference Proceedings of Science and Technology, c. 3, sy 1, ss. 19–23, Ara. 2020, [çevrimiçi]. Erişim adresi: https://izlik.org/JA69XL87NF
ISNAD
Çalışkan, Basri. “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”. Conference Proceedings of Science and Technology 3/1 (01 Aralık 2020): 19-23. https://izlik.org/JA69XL87NF.
JAMA
1.Çalışkan B. Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology. 2020;3:19–23.
MLA
Çalışkan, Basri. “Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$”. Conference Proceedings of Science and Technology, c. 3, sy 1, Aralık 2020, ss. 19-23, https://izlik.org/JA69XL87NF.
Vancouver
1.Basri Çalışkan. Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$. Conference Proceedings of Science and Technology [Internet]. 01 Aralık 2020;3(1):19-23. Erişim adresi: https://izlik.org/JA69XL87NF