On Cyclic Codes of Odd Lengths from the Stable Variety of Regular Cayley Graphs

Abstract

The use of the adjacency matrix of a graph as a generator matrix for some classes of binary codes had been reported and studied. This paper concerns the utilization of the stable variety of Cayley regular graphs of odd order for efficient interconnection networks as studied, in the area of Codes Generation and Analysis. The Use of some succession scheme in the construction of a stable variety of the Cayley regular graph had been considered. We shall enumerate the adjacency matrices of the regular Cayley graphs so constructed which are of odd order (2m + 1),for m ≥ 3 as in [1]. Next, we would show that the Matrices are cyclic and can be used in the generation of cyclic codes of odd lengths.