4 papers · 1 filter
Symmetric Tensor Decompositions over Finite Fields
Giuseppe Cotardo, Ferdinando Zullo
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified wit…
Whitney Numbers of Rank-Metric Lattices and Code Enumeration
Giuseppe Cotardo, Alberto Ravagnani, Ferdinando Zullo
We investigate the Whitney numbers of the first kind of rank-metric lattices, which are closely linked to the open problem of enumerating rank-metric codes having prescribed parame…
The Diagonals of a Ferrers Diagram
Giuseppe Cotardo, Anina Gruica, Alberto Ravagnani
We propose and develop a theory of Ferrers diagrams and their -rook polynomials solely based on their diagonals. We show that the cardinalities of the diagonals of a Ferrers dia…
Rank-Metric Lattices
Giuseppe Cotardo, Alberto Ravagnani
We introduce the class of rank-metric geometric lattices and initiate the study of their structural properties. Rank-metric lattices can be seen as the -analogues of higher-weig…