Perfect Codes Over Induced Subgraphs of Unit Graphs of Ring of Integers Modulo n

The induced subgraph of a unit graph with vertex set as the idempotent elements of a ring R is a graph which is obtained by deleting all non idempotent elements of R. Let C be a subset of the vertex set in a graph Γ. Then C is called a perfect code if for any x, y ∈ C the union of the closed neighbourhoods of x and y gives the the vertex set and the intersection of the closed neighbourhoods of x and y gives the empty set. In this paper, the perfect codes in induced subgraphs of the unit graphs associated with the ring of integer modulo n, Zn that has the vertex set as idempotent elements of Zn are determined. The rings of integer modulo n are classified according to their induced subgraphs of the unit graphs that accept a subset of a ring Zn of different sizes as the perfect codes

SIMULATION MODEL OF THE SOFTWARE FOR WORKING WITH PERFECT CODES BASED ON HAMMING CODE AND GOLE CODE

This article presents an analytical review of noise-tolerant codes, namely, the perfect codes are considered. Ideal codes can be used to encode and decode information, as they have all the desired properties, namely, resistance to interference and ease of implementation. In conclusion, a simulation model of encoding and decoding the information word is developed.