Fish, WashielaFray, RolandMwambene, Eric2023-02-132023-02-132014Fish, W. et al. (2014). Binary codes and partial permutation decoding sets from the odd graphs. Open Mathematics, 12 (9), 1362-1371. 10.2478/s11533-014-0417-y2391-545510.2478/s11533-014-0417-yhttp://hdl.handle.net/10566/8413For 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.enBinary codesAutomorphismPermutation decodingApplied MathematicsArticle