Binary codes and partial permutation decoding sets from the odd graphs
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Date
2014
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Walter de Gruyter
Abstract
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.
Description
Keywords
Binary codes, Automorphism, Permutation decoding, Applied Mathematics
Citation
Fish, 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-y