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Quasi-Cyclic Codes over the Field Fp

Year 2018, Issue: 8, 0 - 0, 01.01.2018

Abstract

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

References

  • 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

Year 2018, Issue: 8, 0 - 0, 01.01.2018

Abstract

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

References

  • 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.
There are 9 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Mustafa Özkan This is me

Figen Öke This is me

Publication Date January 1, 2018
Published in Issue Year 2018 Issue: 8

Cite

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