Block transitive AG codes and the asymptotic problem

M. CHARA

Seminario; ACCESS: Algebraic Coding and Cryptography on the East coast Seminar Series; 2022

In this talk I will discuss the asymptotic behaviour of a class of algebraic geometry codes, which we call block-transitive, that generalizes the classes of transitive and quasi-transitive codes. By using towers of algebraic function fields with either wild or tame ramification, it can be seen that there are sequences of codes in this family attaining the Tsfasman-Vladut-Zink bound over finite fields of square cardinality.If time permits, I will show a construction of cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms to see that cyclic algebraic geometry codes constructed in this way are closely related to cyclic extensions.