5 papers
Betti Numbers and Higher Weight Spectra of Reed-Muller Codes
Sudhir R. Ghorpade, Trygve Johnsen, Rati Ludhani +1
We determine all the Betti numbers of the -ary second order Reed-Muller codes of length , and also of the elongations of matroids associated to these codes. We then use it…
Towards the characterization of minimum weight codewords of Schubert codes
Mrinmoy Datta, Tiasa Dutta, Trygve Johnsen
A conjectural formula for the minimum weight of Schubert codes was conjectured by Ghorpade in 2000. This was established by Xiang in 2008. In 2018, Ghorpade and Singh provided a ne…
On the hull-variation problem of equivalent vector rank metric codes
Duy Ho, Trygve Johnsen
The intersection of a linear code with its dual is called the hull of the code. It is known that, for classical linear codes under the Hamming-metric, the dimension of the hull can…
A q-analogue of delta-matroids and related concepts
Michela Ceria, Trygve Johnsen, Relinde Jurrius
We define and study q-delta-matroids, and q-g-matroids. These objects are analogues, for finite-dimensional vector spaces over finite fields, of delta-matroids and g-matroids arisi…
Linear codes associated to symmetric determinantal varieties; General case
Peter Beelen, Trygve Johnsen, Prasant Singh
The study of linear codes over a finite field of odd cardinality, derived from determinantal varieties obtained from symmetric matrices of bounded rank, was initiated in a recent p…