Construction of Codes By Hyper KU-Valued Functions

  • Samy Mohammed Mostafa
  • Rodyna A. Hosny
  • Reham A. Ghanem
Keywords: Hyper KU-Valued Function, Binary Block Code Of Hyper KU-Valued Functions

Abstract

Coding Theory is a mathematical domain with many applications in Information theory. Various type of codes and their connections with other mathematical objects have been intensively studied. One of these applications, namely connections between binary block codes and BCK-algebras, was recently studied in (Jun, Song,  Flaut ).In this paper, we will focus to one of the recent applications of KU-algebras in the coding theory, namely the Construction of codes by hyper KU-valued functions. First, we shall introduce the notion of hyper KU -valued functions, on a set and  investigate some of it’s related properties. Moreover the codes generated by a hyper  K U- valued function are constructed and several Examples are given. Furthermore, Example with graphs of binary block code constructed from a hyper  KU-algebra and hyper KU-algebra are constructed.

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Author Biographies

Samy Mohammed Mostafa

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Rodyna A. Hosny

Mathematics Department, Faculty of Science,  Zagazig  University, Zagazig , Egypt

Reham A. Ghanem

Department of basic science, Deanship of Preparatory Year and Supporting studies Imam Abdul Rahman Bin Faisal UniversityDammam, Saudi Arabia.

References

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F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49.

S. M. Mostafa, F.Kareem , B. Davvaz, Hyper structure theory applied to KU-algebras. Journal of Hyper structures .6 (2) (2017), 82-95.

Cristina FLAUT, BCK-algebras arising from block codes, arXiv:1408.3598v3

Y. B. Jun, S. Z. Song, Codes based on BCK-algebras, Inform. Sci. 181(2011), 5102-5109

S. M. Mostafa B. Yousse H. A. Jad. Coding theory applied to ku-algebras. Journal of new theory 6 (2015) 43-53

A. Borumand Saeid, H. Fatemidokht, C. Flaut and M. Kuchaki Rafsanjani On Codes based on BCK-algebras, arXiv:1412.8395v1

Published
2019-08-30
How to Cite
Mostafa, S. M., Hosny, R. A., & Ghanem, R. A. (2019). Construction of Codes By Hyper KU-Valued Functions. MathLAB Journal, 3, 140-152. Retrieved from http://purkh.com/index.php/mathlab/article/view/365
Section
Research Articles