3 papers
math.NT2024
Two improvements in Brauer's theorem on forms
Arthur Bik, Jan Draisma, Andrew Snowden
Let be a Brauer field, that is, a field over which every diagonal form in sufficiently many variables has a nonzero solution; for instance, could be an imaginary quadratic…
cs.IT2023
Higher-degree symmetric rank-metric codes
Arthur Bik, Alessandro Neri
Over fields of characteristic unequal to , we can identify symmetric matrices with homogeneous polynomials of degree . This allows us to view symmetric rank-metric codes as l…
math.AG2022
The Geometries of Jordan nets and Jordan webs
Arthur Bik, Henrik Eisenmann
A Jordan net (resp. web) is an embedding of a unital Jordan algebra of dimension (resp. ) into the space of symmetric matrices. We study the geome…