n-ary block codes related to KU-algebras

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...

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

Varieties of Anticommutative n-ary Algebras

A fundamental problem in the theory of n-ary algebras is to determine the correct generalization of the Jacobi identity. This paper describes some computational results on this problem using representations of the symmetric group. It is well known that over a field of characteristic 0 any variety of n-ary algebras can be defined by multilinear identities. In the anticommutative case, it is show...

N-ary Codes, Designs, and Enclosings

n-ary associative algebras, cohomology, free algebras and coalgebras

When n is odd, a cohomology of type Hochschild for n-ary partially associative algebras has been defined in Gnedbaye’s thesis. Unfortunately, the cohomology definition is not valid when n is even. This fact is found again in the computations of the n-ary partially associative free algebra. In this work, we define in a first time two approachs of an Hochschild cohomology for n-ary partially asso...