n-ary block codes related to KU-algebras

Abstract

In this paper, n-ary block codes for KU-algebras and their interconnecting properties in terms of block codes have been given. A construction of n-ary block codes for a given KU-algebra is shown, and it is proved that for each n-ary block code K we can associate a KU-algebra X, such that the constructed n-ary block codes generated by X, i.e. K x , contain the code K as a subset. We have proved that for every n-ary block-code K, there exists a KU-valued function on a KU-algebra which determines K. It is also shown that the KU-algebras associated with an n-ary block code are not unique up to isomorphism. ARTICLE HISTORY KEYWORDS KU-algebra; n-ary block codes; generalized cut functions 2010 MATHEMATICS SUBJECT CLASSIFICATIONS 06F35; 03G25 Definition 2. 1 ([1]): By a KU-algebra we mean an algebra (X, •, 1) of type (2, 0) with a single binary operation • that satisfies the following identities: for any x, y, z ∈ X,

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