Binary codes from the complements of the triangular graphs

Abstract

For n ≥ 4, the complement of the triangular graph denoted by T(n) is the graph of which the vertex-set is Ω^{2}, the set of all 2-subsets of Ω={1,2,…,n}, and any two vertices u and v constitute an edge [u, v] if and only if u⊓v=φ. In this paper the binary codes generated by the rows of the adjacency matrix of T(n) and their corresponding duals are studied. These codes are viewed as subspaces of vector spaces defined on the edge-sets of graphs of order n. Automorphism groups are obtained for these codes, and in the non-trivial cases permutation decoding (PD)-sets of the order of n when n ≡ 1 (mod 4), and of the order of n ² when n ≡ 3 (mod 4) are obtained for the dual code.