Academic Seminar (Course)
Online
25.12.2024 - All Day
SEMINAR:Generalized Spectral Bounds for Quasi-Cyclic and Quasi-Twisted..
Semenov and Trifonov developed a spectral theory for quasi-cyclic codes and formulated a BCH-like minimum distance bound. Their approach was generalized by Zeh and Ling, by using the HT bound. The first spectral bound for quasi-twisted codes was given by Ezerman et. al., which generalizes Semenov-Trifonov and Zeh-Ling bounds, but its overall performance was observed to be worse than the Jensen bound. More recently, an improved spectral bound for quasi-cyclic codes was proposed by Luo et. al., which outperforms the Jensen bound in many cases. In this talk, an overview of Luo et. al. bound as well as an adoptation of this approach to quasi-twisted case with a different proof will be given. Moreover, randomized simulations show that these new generalized spectral bounds yields better minimum distance estimates compared to the Jensen and Ezerman et. al. bounds.