34 citations · 151 across the 19 of their papers we have counts for
24 papers
Generalized Weight Polynomials of Codes through Flats and Orlik-Solomon Algebras of Matroids
Jakob Anderssen, Trygve Johnsen
We present various ways of determining generalized weight polynomials of a matroid , and we recall how one can find the generalized weight spectra of a linear code, given these…
The Euler characteristic, -matroids, and a Möbius function
Trygve Johnsen, Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
We first give two new proofs of an old result that the reduced Euler characteristic of a matroid complex is equal to the Möbius number of the lattice of cycles of the matroid up to…
Codes from symmetric polynomials
Mrinmoy Datta, Trygve Johnsen
We define and study a class of Reed-Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and…
Weight Spectra of Gabidulin Rank-metric Codes and Betti Numbers
Trygve Johnsen, Rakhi Pratihar, Hugues Verdure
We consider -matroids and their associated classical matroids derived from Gabidulin rank-metric codes. We express the generalized rank weights of a Gabidulin rank-metric code i…
Greedy weights for matroids
Trygve Johnsen, Hugues Verdure
We introduce greedy weights of matroids, inspired by those for linear codes. We show that a Wei duality holds for two of these types of greedy weights for matroids. Moreover we sho…
A Polymatroid Approach to Generalized Weights of Rank Metric Codes
Sudhir R. Ghorpade, Trygve Johnsen
We consider the notion of a -polymatroid, due to Shiromoto, and the more general notion of -demi-polymatroid, and show how generalized weights can be defined for them…