Results 1 to 10 of about 4,000 (161)
Generalized Index Coding Problem and Discrete Polymatroids [PDF]
Entropy, 2020 The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids.
Anoop Thomas, Balaji Sundar Rajan
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Binary matroids and local complementation [PDF]
European Journal of Combinatorics, 2014 We introduce a binary matroid M(IAS(G)) associated with a looped simple graph G. M(IAS(G)) classifies G up to local equivalence, and determines the delta-matroid and isotropic system associated with G.
Traldi, Lorenzo
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Powerful sets: a generalisation of binary matroids
The Electronic Journal of Combinatorics, 2017 A set $S\subseteq\{0,1\}^E$ of binary vectors, with positions indexed by $E$, is said to be a \textit{powerful code} if, for all $X\subseteq E$, the number of vectors in $S$ that are zero in the positions indexed by $X$ is a power of 2.
Farr, Graham E., Wang, Andrew Y. Z.
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On n-connected minors of the es-splitting binary matroids
Electronic Journal of Graph Theory and Applications, 2021 The es-splitting operation on an n-connected binary matroid may not yield an n-connected matroid for (n ≥ 3). In this paper, we show that given an n-connected binary matroid M of rank r, the resulting es-splitting binary matroid has an n-connected minor ...
Prashant Pralhad Malavadkar +2 more
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Connections between Linear Complementary Dual Codes, Permanents and Geometry
Mathematics, 2023 Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures.
Adel N. Alahmadi +5 more
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On n-connected splitting matroids
AKCE International Journal of Graphs and Combinatorics, 2019 In general, the splitting operation on a binary matroid M does not preserve the connectivity of M. In this paper, we provide sufficient conditions to preserve n-connectedness of a binary matroid under splitting operation.
Y.M. Borse, Ganesh Mundhe
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Templates for Binary Matroids [PDF]
SIAM Journal on Discrete Mathematics, 2017 A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template. We introduce a preorder on these templates and determine the nontrivial templates that are minimal with respect to this order.
Grace, Kevin, Van Zwam, Stefan H.M.
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Cyclic flats of binary matroids
Advances in Applied Mathematics, 2021 In this paper, first steps are taken towards characterising lattices of cyclic flats $\mathcal{Z}(M)$ that belong to matroids $M$ that can be represented over a prescribed finite field $\mathbb{F}_q$. Two natural maps from $\mathcal{Z}(M)$ to the lattice of cyclic flats of a minor of $M$ are given. Binary matroids are characterised via their lattice of
Grezet, Matthias +4 more
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On the cogirth of binary matroids
Advances in Applied Mathematics, 2023 8 ...
Crenshaw, Cameron, Oxley, James
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The moduli space of matroids [PDF]
, 2018 In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective ...
Baker, Matthew, Lorscheid, Oliver
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