6 papers
Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric
Peter Beelen, Elena Berardini, Anina Gruica +1
Algebraic Geometry (AG) codes (i.e. linear codes from algebraic function fields) in the Hamming metric were proposed by Goppa in 1980 and have been intensively studied ever since.…
On Weierstrass semigroups of maximal Fermat function fields
Peter Beelen, Maria Montanucci, Marie Frank vom Braucke
In this article we explicitly determine the Weierstrass semigroup at any place of some -maximal Fermat function fields , namely for and…
The Geometry of Codes for Random Access in DNA Storage
Anina Gruica, Maria Montanucci, Ferdinando Zullo
Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and relia…
Reed-Solomon Codes Against Insertions and Deletions: Full-Length and Rate- Codes
Peter Beelen, Roni Con, Anina Gruica +2
The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we…
Non-isomorphic subfields of the BM and GGS maximal function fields
Peter Beelen, Tobias Drue, Maria Montanucci +1
In 2016 Tafazolian et al. introduced new families of -maximal function fields and arising as subfields of the first…
Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus,
Peter Beelen, Maria Montanucci, Lara Vicino
In this article we complete the work started in arXiv:2303.00376v1 [math.AG] and arXiv:2404.18808v1 [math.AG], explicitly determining the Weierstrass semigroup at any place and the…