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Binary codes and partial permutation decoding sets from the odd graphs

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Fish W., Fray R., Mwambene E.

Open Mathematics

2014

tom 12

nr 9

1362-1371

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 = /0. 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 $\overline {O(k)} $, is investigated.

Ograniczanie wyników

1 Open Mathematics

1 Fish W.

1 Fray R.

1 Mwambene E.

1 2014

Wyniki wyszukiwania

Binary codes and partial permutation decoding sets from the odd graphs