Ferdinando Zullo

COMBInatorics of NEtwork coding (COMBINE)

Financed by University of Campania "Luigi Vanvitelli" (Bando giovani ricercatori 2022)

The 2000 paper by Ahlswede, Cai, Li, and Yeung revolutionized network information transmission, introducing the concept of information flow. This project's goals are to study code parameter bounds, create optimal network codes, and design efficient encoding and decoding algorithms. These efforts aim to enhance both theoretical understanding and practical applications of network coding with the use of combinatorial methods.

PI: Ferdinando Zullo

co-PI: Olga Polverino

Members:

Chiara Castello
Maria Ferrara
Suliman Khan
Vito Napolitano
Mariapia Raimondo
Paolo Santonastaso
Antonio Tortora

Activities

Postdoctoral position (6 months) - Paolo Santonastaso
One-day event [31 October 2023]: Coding theory and cryptography meetup
Workshop [14-16 February 2024]: Open Problems on Rank-Metric Codes (OpeRa2024)
Conference [5-6 September 2025]: Annual Conference "Cryptography and Coding Theory UMI Group"

Papers

Constructions and equivalence of Sidon spaces, C. Castello, O. Polverino, P. Santonastaso and F. Zullo, Journal of Algebraic Combinatorics 54 (2023) -> arxiv -> JACO
Clubs and their applications, V. Napolitano, O. Polverino, P. Santonastaso and F. Zullo, SIAM Journal on Applied Algebra and Geometry 8(3) (2024), 493-518 -> arxiv -> SIAGA
New scattered quadrinomials, V. Smaldore, C. Zanella and F. Zullo, Linear Algebra and its Applications 702 (2024), 143-160 -> arxiv -> LAA
Geometric dual and sum-rank minimal codes, M. Borello and F. Zullo, Journal of Combinatorial Designs -> arxiv -> JCD
Maximum flag-rank distance codes, G. Alfarano, A. Neri and F. Zullo, Journal Combinatorial Theory, Series A 207 (2024), 105908 -> arxiv -> JCTA
Saturating linear sets in PG(2,q^4) , F. Zullo, Finite Fields and Their Applications 97 (2024), 102447 -> arxiv -> FFA
On subspace designs, P. Santonastaso and F. Zullo, EMS Surveys in Mathematical Sciences 11(1) (2024), 1-62 -> arxiv ->EMSSurvey
Maximum weight codewords of a linear rank metric code, O. Polverino, P. Santonastaso and F. Zullo, SIAM Journal on Discrete Mathematics -> arxiv
Generalised Evasive Subspaces, A. Gruica, A. Ravagnani, J. Sheekey and F. Zullo, Journal of Combinatorial Designs-> arxiv -> JCD

Waring identifiable subspaces over finite fields, M. Lavrauw and F. Zullo -> arxiv
On the stabilizer of the graph of linear functions over finite fields, V. Smaldore, C. Zanella and F. Zullo -> arxiv
Using multi-orbit cyclic subspace codes for constructing optical orthogonal codes, F. Ozbudak, P. Santonastaso and F. Zullo -> arxiv
Full weight spectrum one-orbit cyclic subspace codes, C. Castello, O. Polverino and F. Zullo -> arxiv
On perfect symmetric rank-metric codes, Usman Musharraf and F. Zullo -> arxiv
Representability of the direct sum of uniform q-matroids, G. Alfarano, R. Jurrius, A. Neri and F. Zullo -> arxiv
On generalized Sidon spaces, C. Castello -> arxiv
Completely decomposable rank-metric codes, P. Santonastaso -> arxiv
On MSRD codes, h-designs and disjoint maximum scattered linear sets, P. Santonastaso and J. Sheekey -> arxiv
Prime power residues and blocking sets, M. Bhawesh and P. Santonastaso, submitted
Stability and ω-categocity of skew braces, M. Ferrara, M. Invitti, M. Trombetti and F. O. Wagner, in preparation

Conference papers

On one-orbit cyclic subspace codes in Gq(n,3), C. Castello, O. Polverino and F. Zullo, ISIT 2024 -> arxiv -> IEEE
Two-weight rank-metric codes, O. Polverino, P. Santonastaso, J. Sheekey and F. Zullo, ISIT 2024 -> arxiv -> IEEE
On r-fat polynomials, O. Polverino, P. Santonastaso and F. Zullo, WAIFI 2024
On the maximum weight codewords of linear rank-metric codes, O. Polverino, P. Santonastaso and F. Zullo, WCC2024
Stabilizers of graphs of linear functions and rank-metric codes, V. Smaldore, C. Zanella and F. Zullo, WCC2024
Identifying glyphs in rock engravings using statistical information, S. Crisci, V. De Simone, A. Diana and F. Zullo, accepted for publication CEUR Workshop Proceedings Amalart 2024
A nonnegative matrix factorization-based data augmentation procedure for two-dimensional data, S. Crisci, V. De Simone and F. Zullo accepted for publication CEUR Workshop Proceedings Amalart 2024