Ternary codes from some reflexive uniform subset graphs

Fish, W.; Key, J. D.; Mwambene, E.

doi:10.1007/s00200-014-0233-4

Cited by 6 publications

(1 citation statement)

References 7 publications

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“…For reflexive graphs whose codes possess these properties and which are related to strongly regular graphs, see [33] for the binary codes from the strongly regular graph related to the Conway group Co 2 , [34] for the binary codes of the strongly regular graph related to the simple group Ru of Rudvalis, and [35] for the ternary codes of the complement of the Higman-Sims graph. Other classes of reflexive graphs also yielded interesting codes, see for example [21,22] for the study of the binary and ternary codes from reflexive uniform subset graphs on the 3-element subsets of a set of size n.…”

Section: Introductionmentioning

confidence: 99%

On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $

Le¹,

Rodrigues²

2023

AMC

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<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M2">\begin{document}$ G_2(q) $\end{document}</tex-math></inline-formula> be a Chevalley group of type <inline-formula><tex-math id="M3">\begin{document}$ G_2 $\end{document}</tex-math></inline-formula> over a finite field <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{F}_q $\end{document}</tex-math></inline-formula>. Considering the <inline-formula><tex-math id="M5">\begin{document}$ G_2(q) $\end{document}</tex-math></inline-formula>-primitive action of rank <inline-formula><tex-math id="M6">\begin{document}$ 3 $\end{document}</tex-math></inline-formula> on the set of <inline-formula><tex-math id="M7">\begin{document}$ \frac{q^3(q^3-1)}{2} $\end{document}</tex-math></inline-formula> hyperplanes of type <inline-formula><tex-math id="M8">\begin{document}$ O_{6}^{-}(q) $\end{document}</tex-math></inline-formula> in the <inline-formula><tex-math id="M9">\begin{document}$ 7 $\end{document}</tex-math></inline-formula>-dimensional orthogonal space <inline-formula><tex-math id="M10">\begin{document}$ {{\rm{PG}}}(7, q) $\end{document}</tex-math></inline-formula>, we study the designs, codes, and some related geometric structures. We obtained the main parameters of the codes, the full automorphism groups of these structures, and geometric descriptions of the classes of minimum weight codewords.</p>

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Section: Introductionmentioning

confidence: 99%

On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $

Le¹,

Rodrigues²

2023

AMC

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LCD codes from adjacency matrices of graphs

Key

Rodrigues

2017

AAECC

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Codes from Adjacency Matrices of Uniform Subset Graphs

Fish

Key

Mwambene

2017

Graphs and Combinatorics

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Studies of the p-ary codes from the adjacency matrices of uniform subset graphs Γ (n, k, r) and their reflexive associates have shown that a particular family of codes defined on the subsets are intimately related to the codes from these graphs. We describe these codes here and examine their relation to some particular classes of uniform subset graphs. In particular we include a complete analysis of the p-ary codes from Γ (n, 3, r) for p ≥ 5, thus extending earlier results for p = 2, 3.

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Ternary codes from some reflexive uniform subset graphs

Cited by 6 publications

References 7 publications

On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $

On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $

LCD codes from adjacency matrices of graphs

Codes from Adjacency Matrices of Uniform Subset Graphs

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