2025/09/23 by Régis Blache, Blache, Régis, Emmanuel Hallouin +1
Computer Science · Engineering · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2509.18698
openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part, we consider evaluation codes on some such surfaces; we first estimate their parameters, then we construct asymptotically good families of such codes, and we show that their asymptotic parameters are better than the ones of the corresponding product codes. We also consider local properties of these codes.