Generalized Cut Functions and n-Ary Block Codes on UP-Algebras

Abstract

In this paper, the work is comprised of n-ary block codes for UP-algebras and their interrelated properties. n-ary block codes for a known UP-algebra is constructed and further it is shown that for each n-ary block code U, it is easy to associate a UP-algebra U in such a way that the newly constructed n-ary block codes generated by U, i.e., Ux, contain the code U as a subset. We define a UP-algebra valued function on a set say X, then we prove that for every n-ary block-code U, a generalized UP-valued cut function exists that determines U. We have also proved that the UP-algebras associated to an n-ary block code are not unique up to isomorphism.