Coding theory and hyper BCK-algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Yaound´e 1, P.O.Box 47, Yaound´e, Cameroon

2 Department of Mathematics, Higher Teacher Training College, University of Yaound´e 1, P.O.Box 47, Yaound´e, Cameroon

3 Department of Mathematics, University of Dschang, P.O.Box 67, Dschang, Cameroon

Abstract

In this paper we define the notion of a hyper BCK valued function on a set and investigate some of it’s related properties as Y.B. Jun, S.Z. Song and C. Flaut have done for a BCK-algebras. We construct the codes generated by a hyper BCK valued function and provide an algorithm which allow to find a hyper BCK-algebra starting from a given binary block code. Moreover we establish the link between the hyper BCK-algebra constructed from a binary block code and hyper BCK-ideal on a hyper BCK-algebra.

Keywords

References

[1] T.S. Atamewoue, Y.B. Jun, C. Lele, S. Ndjeya, and S.Z. Song, Codes based on residuated lattices, Commun. Korean Math. Soc., 31 (2016), 27–40.
[2] R.A. Borzooei and M. Bakhshi, Some Results in Hyper BCK-algebras, Quasi-groups and Related Systems 11 (2004), 9–24.
[3] C. Flaut, BCK-algebras Arising from Block Codes, J. Intell. Fuzzy Syst., 28
(2015), 1829–1833.
[4] K. Iseki, S. Tanaka, An Introduction to the Theory of BCK-algebras, Math. Japonica, 23 (1978), 1–26.
[5] Y. B. Jun and S. Z. Song, Codes based on BCK-algebras, Inform. Sci., 181 (2011), 5102–5109.
[6] Y.B. Jun, M.M. Zahedi, X.L. Xin and R.A. Borzoei, On Hyper BCK-algebras,Italian Journal of Pure and Applied Mathematics, 8 (2000), 127–136.
[7] F. Marty, Sur une generalization de la notion de groupe, 8iem congres Math. Scandinaves,Stockholm, (1934), 45–49.
[8] E.H. Roh, Q. Zhang and Y.B.Jun,Some Results in Hyper BCK-algebras,Scien-tiae Mathematicae Japonica,5(2001),265–272. 
Journal of Hyperstructures
Volume 7, Issue 2
December 2018
Pages 82-93

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