Special Session 29
Finite Geometry, Galois Fields and Their Impact on Contemporary Coding Theory
Organizers: Giovanni Longobardi (University of Naples “Federico II”, Italy), Daniela Alves de Oliveira (Federal University of Minas Gerais, Brazil), Giovanni Giuseppe Grimaldi (University of Perugia, Italy)
MSC codes: 94B24
Description:
Finite geometry and finite fields play a central role in contemporary coding theory, providing powerful tools for the construction and analysis of error-correcting codes. In particular, Galois geometries offer a natural framework in which the algebraic and
combinatorial properties of codes can be studied and exploited.
This special session aims to explore these deep connections by highlighting recent developments and by providing a contemporary perspective on their role in the advancement of coding theory and combinatorics. A central goal is to show how
these structures serve not merely as technical tools, but as a structural setting that connects different families of codes, including linear codes, rank-metric codes and subspace codes, as well as to illustrate how geometric methods are linked to
applications in data storage and network coding.
We wish to invite contributions presenting recent results and developments, including but not limited to the following topics:
- Algebraic geometry codes
- Algebraic varieties over finite fields
- Galois geometries and projective spaces over finite fields
- Graph theory methods in coding theory
- Linear codes and geometric constructions
- Rank-metric codes and subspace codes
- Related algebraic and combinatorial structures
