2024/03/27 by Junmin An, Jon-Lark Kim, An, Junmin +1
Computer Science · #94B27 #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2403.18231
openalex publication_date 2024/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Chara et al. introduced conorm codes defined over algebraic geometry codes, but the hulls of conorm codes were not determined yet. In this paper, we study the dimension of the hull of conorm codes using the method introduced by Camps et al. For an algebraic geometry code C:=C_\mathscrL(D, G), we consider the divisor gcd(G, H), where H is the divisor satisfying C_\mathscrL(D, G)^⊥=C_\mathscrL(D, H). Given an extension F'/\mathbbFqt of an algebraic function field F/\mathbbFq, we assume that the divisor gcd(G, H) is non-special. If the degree of gcd(G, H) is greater than 2g-2+t\over [F':F]°Diff(F'/F), then we have determined the exact dimension of the hull of the conorm of C. If not, we have determined the lower bound of the dimension of the hull of the conorm of C. We provide some examples for the dimension of the hull of certain conorm codes of AG codes defined over a rational function field.