6 papers
Constructions of Rank-Metric Codes of Small Tensor Rank
Matteo Bonini, Eimear Byrne, Giuseppe Cotardo
Rank-metric codes are subspaces of matrices over finite fields endowed with the rank metric and admit a natural tensorial representation. The tensor rank provides a measure of the…
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…
Weak Composition Lattices and Ring-Linear Anticodes
Jessica Bariffi, Drisana Bhatia, Giuseppe Cotardo +1
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties…
Quantum Anticodes
ChunJun Cao, Giuseppe Cotardo, Brad Lackey
This work introduces a symplectic framework for quantum error correcting codes in which local structure is analyzed through an anticode perspective. In this setting, a code is trea…
Multishot Capacity of Networks with Restricted Adversaries
Giuseppe Cotardo, Gretchen L. Matthews, Alberto Ravagnani +1
We investigate adversarial network coding and decoding, focusing on the multishot regime and when the adversary is restricted to operate on a vulnerable region of the network. Erro…
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…