Construction of Codes By Hyper KU-Valued Functions
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.
C. Prabpayak and U.Leerawat, On ideals and congruence in KU-algebras, scientia Magna in- ternational book series, Vol. 5(2009), No.1, 54-57.
C.Prabpayak and U.Leerawat, On isomorphisms of KU-algebras, scientia Magna international book series, 5(2009), no .3, 25-31.
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
Copyright (c) 2019 Samy Mohammed Mostafa, Rodyna A. Hosny, Reham A. Ghanem
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.