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math.AG2024
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…
math.CO2024
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…
math.CO2024
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…