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., U x , 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.