Browsing by Author "Fish, Washiela"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Binary codes and partial permutation decoding sets from the odd graphs
    (Walter de Gruyter, 2014) Fish, Washiela; Fray, Roland; Mwambene, Eric
    For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ω{k} , the set of all k-subsets of Ω = {1, 2, . . . , 2k + 1}, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = ∅. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k) and the code from its graph-theoretical complement O(k), is investigated.