39 citations · 136 across the 26 of their papers we have counts for
32 papers
Number Theoretical Locally Recoverable Codes
Andrea Ferraguti, Dorian Goldfeld, Giacomo Micheli
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes over a product o…
On complete -arcs
Luca Bastioni, Giacomo Micheli
Let be a positive integer and be a prime power. For large finite base fields , we show that any curve can be used to produce a complete -arc as long as some…
Differential biases, -differential uniformity, and their relation to differential attacks
Daniele Bartoli, Lukas Kölsch, Giacomo Micheli
Differential cryptanalysis famously uses statistical biases in the propagation of differences in a block cipher to attack the cipher. In this paper, we investigate the existence of…
Optimal locally recoverable codes with hierarchy from nested -adic expansions
Austin Dukes, Giacomo Micheli, Vincenzo Pallozzi Lavorante
In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015co…
Local to global principle over number fields for higher moments
Giacomo Micheli, Severin Schraven, Simran Tinani +1
The local to global principle for densities is a very convenient tool proposed by Poonen and Stoll to compute the density of a given subset of the integers. In this paper we provid…
Optimal Selection for Good Polynomials of Degree up to Five
Austin Dukes, Andrea Ferraguti, Giacomo Micheli
Good polynomials are the fundamental objects in the Tamo-Barg constructions of Locally Recoverable Codes (LRC). In this paper we classify all good polynomials up to degree , pro…