# Binary codes and partial permutation decoding sets from the odd graphs

Washiela Fish; Roland Fray; Eric Mwambene

Open Mathematics (2014)

- Volume: 12, Issue: 9, page 1362-1371
- ISSN: 2391-5455

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topWashiela Fish, Roland Fray, and Eric Mwambene. "Binary codes and partial permutation decoding sets from the odd graphs." Open Mathematics 12.9 (2014): 1362-1371. <http://eudml.org/doc/269206>.

@article{WashielaFish2014,

abstract = {For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, 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.},

author = {Washiela Fish, Roland Fray, Eric Mwambene},

journal = {Open Mathematics},

keywords = {Odd graphs; Binary codes; Automorphism group; Permutation decoding; odd graphs; binary codes; automorphism group; permutation decoding},

language = {eng},

number = {9},

pages = {1362-1371},

title = {Binary codes and partial permutation decoding sets from the odd graphs},

url = {http://eudml.org/doc/269206},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Washiela Fish

AU - Roland Fray

AU - Eric Mwambene

TI - Binary codes and partial permutation decoding sets from the odd graphs

JO - Open Mathematics

PY - 2014

VL - 12

IS - 9

SP - 1362

EP - 1371

AB - For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, 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.

LA - eng

KW - Odd graphs; Binary codes; Automorphism group; Permutation decoding; odd graphs; binary codes; automorphism group; permutation decoding

UR - http://eudml.org/doc/269206

ER -

## References

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