Binary codes and partial permutation decoding sets from the odd graphs

dc.contributor.authorFish, Washiela
dc.contributor.authorFray, Roland
dc.contributor.authorMwambene, Eric
dc.date.accessioned2023-02-13T07:56:11Z
dc.date.available2023-02-13T07:56:11Z
dc.date.issued2014
dc.description.abstractFor 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.en_US
dc.identifier.citationFish, 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-yen_US
dc.identifier.issn2391-5455
dc.identifier.uri10.2478/s11533-014-0417-y
dc.identifier.urihttp://hdl.handle.net/10566/8413
dc.language.isoenen_US
dc.publisherWalter de Gruyteren_US
dc.subjectBinary codesen_US
dc.subjectAutomorphismen_US
dc.subjectPermutation decodingen_US
dc.subjectApplied Mathematicsen_US
dc.titleBinary codes and partial permutation decoding sets from the odd graphsen_US
dc.typeArticleen_US

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