A Binary Block Code Generated by JU-Algebras
Ranelyn I. Ral *
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Ann Leslie V. Flores
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
*Author to whom correspondence should be addressed.
Abstract
Studies on the binary block codes generated by some ordered algebraic structures have been the interest of many researchers. In this paper, we study the binary block code generated by an arbitrary JU-algebra and investigate some of its properties. For this intent, we introduce the notion of a JU function \(\phi\) on a nonempty set P into a JU-algebra X, and by using that concept, j-functions and j-subsets of P for an arbitrary element j on a JU-algebra X are investigated. Furthermore, we define a new order on the generated code C based on the JU-algebra X, and show that every finite JU-algebra with its order and the corresponding generated code C with the defined order have the same structures. Finally, we generate a JU-algebra from a particular set of binary block code.
Keywords: JU-algebra, JU-function, j-function, j-subset, binary block code, coding theory