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Erschienen in:
24.08.2017 | Foundations
Some connections between BCK-algebras and n-ary block codes
Erschienen in: Soft Computing | Ausgabe 1/2018
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Abstract
In general, when block codes are defined, the used alphabet is not binary. It is used an alphabet with n elements, \(n\ge 2,\) identified usually with the set \( A_{n}=\{0,1,2,\ldots ,n-1\}\). Recently, some papers were devoted to the study of the connections between binary block codes and BCK-algebras. These codes are called n-ary block codes. In this paper, we try to generalize these results to n-ary block codes, providing an algorithm which allows us to construct a BCK-algebra from a given n-ary block code. For this purpose, we will prove that to each n-ary block code V we can associate a BCK-algebra X, such that the n-ary block code generated by \(X,V_{X},\)contains the code V as a subset and we will find in what circumstances the converse is also true.