6 papers
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…
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…
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…
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: Even Rank Case
Peter Beelen, Trygve Johnsen, Prasant Singh
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weigh…