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Quasi-Cyclic Codes over the Field Fp

Yıl 2018, Sayı: 8, 0 - 0, 01.01.2018

Öz

Bu çalışmada, katsayıları F cisminde iki değişkenli halkalar üzerinde cyclic kodların görüntüleri tespit edilmiştir. Belirli koşullar altında iki değişkenli özel bir halka tanımlanmıştır. Bu halkalar üzerinde cyclic kodların Gray görüntüleri incelenmiştir. Gray dönüşümü yoluyla bu halkalar üzerindeki kodlar ve bir değişkenli sonlu zincir halkası üzerindeki kodlar elde edilmiştir. Sonlu zincir halkasından sonlu bir cisme başka Gray dönüşümü tanımlanmış ve sonra cyclic kodların görüntüleri elde edilmiştir. n uzunluğundaki R üzerinde bir cyclic kodun Gray görüntüsü bulunmuştur

Kaynakça

  • Özkan M, Öke F(2016), Some Special Codes Over F F v3F3 u32F3, Mathematical Sciences u23F3, Mathematical Sciences and Applications E-Notes .Vol. 4 No 1,pp 40-44. Xioafang X (2013), 1(
  • )v-constacyclic codes over IF  uIF2vIF2,Computer Engineering and Applications,49, 12, 77-79. Udomkavanich P, Jitman S (2009) , On the Gray Image of ( um)-Cyclic Codes .uF pk pk FkuFk mF pk
  • Roman S (1992), Coding and Information Theory, Graduate Texts in Mathematics, Springer Verlag.
  • Özkan M, Öke F (2017), Gray images of (1 constacyclic codes over a particular ring, v)
  • Palestine Journal of Mathematics. Vol. 6(S.I.2), 241-245. Karadeniz S,Yıldız B (2011), On 1 (1 constacyclic codes over F  uF2F2 uvF2,Journal vF2 of the Franklin Institude , 348, 2625-2632.
  • Özkan M, Öke F (2017) ,Repeat codes, Even codes, Odd codes and Their equivalence
  • General Letters in Mathematics, Vol. 2, No :1, pp : 110-118. Özkan M, Öke F (2017) ,Codes defined via especial matrices over the ring and Hadamard codes, Mathematical Sciences and Applications E-Notes, Volume 5, No :1, pp : 93-98.
  • Özkan M, Öke F(2016) ,A relation between Hadamard codes and some special codes over
  • F2+uF2, App.Mathematics and Inf. Sci. Vol.10, No: 2, pp : 701-704.

Quasi-Cyclic Codes over the Field F p

Yıl 2018, Sayı: 8, 0 - 0, 01.01.2018

Öz

In this study, images of cyclic codes in two variable rings with coefficient field F are detected. p are detected. A special ring in two variables is defined under certain conditions. The Gray images of the cyclic codes over this ring are investigated. Relations between the codes over this ring and the codes over a finite chain ring in one variable are obtained via a Gray map. Another Gray map from the finite chain ring to a finite field is defined and then the images of cyclic codes are obtained.It is obtained that the Gray image of a cyclic code over R with length n

Kaynakça

  • Özkan M, Öke F(2016), Some Special Codes Over F F v3F3 u32F3, Mathematical Sciences u23F3, Mathematical Sciences and Applications E-Notes .Vol. 4 No 1,pp 40-44. Xioafang X (2013), 1(
  • )v-constacyclic codes over IF  uIF2vIF2,Computer Engineering and Applications,49, 12, 77-79. Udomkavanich P, Jitman S (2009) , On the Gray Image of ( um)-Cyclic Codes .uF pk pk FkuFk mF pk
  • Roman S (1992), Coding and Information Theory, Graduate Texts in Mathematics, Springer Verlag.
  • Özkan M, Öke F (2017), Gray images of (1 constacyclic codes over a particular ring, v)
  • Palestine Journal of Mathematics. Vol. 6(S.I.2), 241-245. Karadeniz S,Yıldız B (2011), On 1 (1 constacyclic codes over F  uF2F2 uvF2,Journal vF2 of the Franklin Institude , 348, 2625-2632.
  • Özkan M, Öke F (2017) ,Repeat codes, Even codes, Odd codes and Their equivalence
  • General Letters in Mathematics, Vol. 2, No :1, pp : 110-118. Özkan M, Öke F (2017) ,Codes defined via especial matrices over the ring and Hadamard codes, Mathematical Sciences and Applications E-Notes, Volume 5, No :1, pp : 93-98.
  • Özkan M, Öke F(2016) ,A relation between Hadamard codes and some special codes over
  • F2+uF2, App.Mathematics and Inf. Sci. Vol.10, No: 2, pp : 701-704.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Research Article
Yazarlar

Mustafa Özkan Bu kişi benim

Figen Öke Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2018
Yayımlandığı Sayı Yıl 2018 Sayı: 8

Kaynak Göster

APA Özkan, M., & Öke, F. (2018). Quasi-Cyclic Codes over the Field Fp. Journal of New Results in Engineering and Natural Sciences(8).