Codewords generated by UP-valued functions

Ronnason Chinram; Aiyared Iampan; Ronnason Chinram; Aiyared Iampan

doi:10.3934/math.2021280

AIMS Mathematics

2021, Volume 6, Issue 5: 4771-4785. doi: 10.3934/math.2021280

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Research article

Codewords generated by UP-valued functions

Ronnason Chinram ¹,
Aiyared Iampan ^{2,3
,
,}

1.
Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
2.
Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand
3.
Unit of Excellence in Mathematics, University of Phayao, Phayao 56000, Thailand

Received: 17 November 2020 Accepted: 22 February 2021 Published: 25 February 2021
MSC : 06F35, 03G25, 94B05

The concept of a UP-valued function on a nonempty set was introduced by Ansari et al. [3]. Codewords in a binary block-code generated by a UP-valued function are established and some interesting results are obtained. Finally, we prove that every finite UP-algebra $ A $ which has the order less than or equal to the order of a finite set $ X $ determines a binary block-code $ V $ such that $ (A, \leq) $ is isomorphic to $ (V, \preceq) $.
- UP-algebra,
- UP-valued function,
- cut function,
- codeword,
- binary block-code
Citation: Ronnason Chinram, Aiyared Iampan. Codewords generated by UP-valued functions[J]. AIMS Mathematics, 2021, 6(5): 4771-4785. doi: 10.3934/math.2021280

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Abstract

The concept of a UP-valued function on a nonempty set was introduced by Ansari et al. [3]. Codewords in a binary block-code generated by a UP-valued function are established and some interesting results are obtained. Finally, we prove that every finite UP-algebra $ A $ which has the order less than or equal to the order of a finite set $ X $ determines a binary block-code $ V $ such that $ (A, \leq) $ is isomorphic to $ (V, \preceq) $.

References

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