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Belirli Halkalar ve Grup Kodlar

Year 2018, Issue: 8, 25 - 30, 01.01.2018

Abstract

Bu çalışmada, belirli halkaların yapısı ve idealleri hakkında bilgi verilmektedir. Sonlu zincir halkalarının işlemleri ve yapıları ele alınmaktadır. Bu halkaların idealleri sınıflandırılmaktadır. Kodlama teorisinde yeni ve daha iyi kod yazmak için yeni yapılara ihtiyaç duyulmaktadır. Yazılacak kodların alt yapıları burada yazılan yapılarla incelenmektedir. Halkaların yapılarının yeni yazılabilir kodlara nasıl referans olabileceği açıklanmaktadır. Ayrıca kodlama teorisinde öncelikli olmayan grup kodlarıyla daha temel yapıda yazılabilecek iyi kodlara değinilmiştir. Kodlama teorisinde grup kodlarının önemi belirtilmek üzere incelenmiş ve bağlantıları kurulmuştur

References

  • [1] Özkan M, Öke F (2016). Some Special Codes Over 2 F vF uF u F 3 3 3 3    . Mathematical Sciences and Applications E-Notes, Vol. 4 No 1, pp 40-44.
  • [2] Roman S (1992). Coding and Information Theory. Graduate Texts in Mathematics, Springer Verlag.
  • [3] Özkan M, Öke F (2017). Gray images of (1 )   v constacyclic codes over a particular ring. Palestine Journal of Mathematics, Vol. 6(S.I.2), 241-245.
  • [4] 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.
  • [5] 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.
  • [6] Özkan M, Öke F (2016). A relation between Hadamard codes and some special codes over F uF 2 2  . App.Mathematics and Inf. Sci. Vol.10, No: 2, pp : 701-704.
  • [7] Huffman W.C, Pless V (2003). Fundamentals of Error Correcting Codes, Cambridge.
  • [8] Vermani L.R (1996). Elements of Algebraic Coding Theory, Chapman Hall, India

Certain Rings and Group Codes

Year 2018, Issue: 8, 25 - 30, 01.01.2018

Abstract

In this study, the structure of certain rings and information about their ideals is given. The operations and the structures of the finite chain rings are discussed. The ideals of these rings are classified. New structures are needed to write new and better codes in coding theory. Substructures of the codes to be written are studied with the structures written here. It is revealed how the structures of the rings can be referenced to the newly writable codes. Moreover it is mentioned about the good codes which can be written in the more basic structure with the group codes which are not very preliminary in the coding theory. The significance of group codes in the coding theory is studied to be indicated and their correlations are established.

References

  • [1] Özkan M, Öke F (2016). Some Special Codes Over 2 F vF uF u F 3 3 3 3    . Mathematical Sciences and Applications E-Notes, Vol. 4 No 1, pp 40-44.
  • [2] Roman S (1992). Coding and Information Theory. Graduate Texts in Mathematics, Springer Verlag.
  • [3] Özkan M, Öke F (2017). Gray images of (1 )   v constacyclic codes over a particular ring. Palestine Journal of Mathematics, Vol. 6(S.I.2), 241-245.
  • [4] 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.
  • [5] 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.
  • [6] Özkan M, Öke F (2016). A relation between Hadamard codes and some special codes over F uF 2 2  . App.Mathematics and Inf. Sci. Vol.10, No: 2, pp : 701-704.
  • [7] Huffman W.C, Pless V (2003). Fundamentals of Error Correcting Codes, Cambridge.
  • [8] Vermani L.R (1996). Elements of Algebraic Coding Theory, Chapman Hall, India
There are 8 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Mustafa Özkan

Burcu Öztürk This is me

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

Cite

APA Özkan, M., & Öztürk, B. (2018). Belirli Halkalar ve Grup Kodlar. Journal of New Results in Engineering and Natural Sciences(8), 25-30.