Some connections between BCK-algebras and n-ary block codes

Some connections between BCK-algebras and n-ary block codes

Y. Imai and K. Iseki introduced BCK-algebras in 1966, through the paper [Im, Is; 66], as a generalization of the concept of set-theoretic difference and propositional calculi. This class of BCK-algebras is a proper subclass of the class of BCI-algebras and has many applications to various domains of mathematics. One of the recent applications of BCK-algebras was given in the Coding Theory. In t...

Some connections between binary block codes and Hilbert algebras

In this paper, we will study some connections between Hilbert algebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using binary block-codes, we can provide examples of classes of Hilbert algebras with some properties, in our case, classes of semisimple Hilbert algebras and classes of...

BCK-algebras arising from block codes

In this paper, we will provide an algorithm which allows us to find a BCK-algebra starting from a given binary block code.

On Codes based on BCK-algebras

In this paper, we present some new connections between BCKalgebras and binary block codes.

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism