14 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…
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…
Multishot Adversarial Network Decoding
Giuseppe Cotardo, Gretchen L. Matthews, Alberto Ravagnani +1
We investigate adversarial network coding and decoding focusing on the multishot regime. Errors can occur on a proper subset of the network edges and are modeled via an adversarial…
Zeta Functions for Tensor Codes
Giuseppe Cotardo
In this work we introduce a new class of optimal tensor codes related to the Ravagnani-type anticodes, namely the -tensor maximum rank distance codes. We show that it extends th…
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…
Tensor Codes and their Invariants
Eimear Byrne, Giuseppe Cotardo
In 1991, Roth introduced a natural generalization of rank metric codes, namely tensor codes. The latter are defined to be subspaces of -tensors where the ambient space is endowe…
Bilinear Complexity of 3-Tensors Linked to Coding Theory
Eimear Byrne, Giuseppe Cotardo
A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a…
Parameters of Codes for the Binary Asymmetric Channel
Giuseppe Cotardo, Alberto Ravagnani
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetri…
Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions
Eimear Byrne, Giuseppe Cotardo, Alberto Ravagnani
In this paper we introduce a new class of extremal codes, namely the -BMD codes. We show that for this family several of the invariants are determined by the parameters of the u…