Séminaire de Théorie Algorithmique des Nombres
Additive Twisted Codes: New Distance Bounds and Infinite Families of Quantum Codes
Reza Dasbasteh
( University of Navarra )salle 2
le 24 septembre 2024 à 11:00
In this talk, we present a new construction of quantum codes that enables the integration of a broader class of classical codes into the mathematical framework of quantum stabilizer codes. Next, we discuss new connections between twisted codes and linear cyclic codes and provide novel bounds for the minimum distance of twisted codes. We demonstrate that classical tools, such as the Hartmann-Tzeng minimum distance bound, are applicable to twisted codes. This has led to the discovery of five new infinite families and many other examples of record-breaking, and sometimes optimal, binary quantum codes. Additionally, we explore the role of the value on the parameters of twisted codes and present new findings regarding the construction of twisted codes with different values but identical parameters.