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Article Dans Une Revue Designs, Codes and Cryptography Année : 2023

Constructions of New q-Cryptomorphisms

Résumé

In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which are described as matroid cryptomorphisms. A q-matroid is a q-analogue of a matroid where subspaces play the role of the subsets in the classical theory. In this article we establish cryptomorphisms of q-matroids. In doing so we highlight the difference between classical theory and its q-analogue. We introduce a comprehensive set of q-matroid axiom systems and show cryptomorphisms between them and existing axiom systems of a q-matroid. These axioms are described as the rank, closure, basis, independence, dependence, circuit, hyperplane, flat, open space, spanning space, non-spanning space, and bi-colouring axioms.

Dates et versions

hal-04363827 , version 1 (26-12-2023)

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Citer

Eimear Byrne, Michela Ceria, Sorina Ionica, Relinde Jurrius, Elif Saçikara. Constructions of New q-Cryptomorphisms. Designs, Codes and Cryptography, 2023, 91 (2), pp.451-473. ⟨10.1007/s10623-022-01087-3⟩. ⟨hal-04363827⟩
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