3 citations · 4 across the 5 of their papers we have counts for
5 papers
On Representing Matroids via Modular Independence
Koji Imamura, Keisuke Shiromoto
We study a matrix-based notion of matroid representation over local commutative rings obtained by replacing linear independence with modular independence. This construction always…
Matroids and Codes with the Rank Metric
Keisuke Shiromoto
We study the relationship between a q-analogue of matroids and linear codes with the rank metric in the vector space of matrices with entries in a finite field. We prove a Greene t…
A generalization of Kung's theorem
Trygve Johnsen, Keisuke Shiromoto, Hugues Verdure
We give a generalization of Kung's theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all i=k+1…
On the covering dimension of a linear code
Thomas Britz, Keisuke Shiromoto
The critical exponent of a matroid is one of the important parameters in matroid theory and is related to the Rota and Crapo's Critical Problem. This paper introduces the covering…
Generalizations of Wei's Duality Theorem
Thomas Britz, Bård Heiseldel, Trygve Johnsen +2
Wei's celebrated Duality Theorem is generalized in several ways, expressed as duality theorems for linear codes over division rings and, more generally, duality theorems for matroi…