SEMINAR:Generalized Spectral Bounds for Quasi-Cyclic and Quasi-Twisted..

Guest: Buket Özkaya, METU

Title: Generalized Spectral Bounds for Quasi-Cyclic and Quasi-Twisted Codes (MATH, PHYS)

Date/Time: December 25, 2024, 13:40

Location: https://zoom.us/j/98438990666?pwd=bHNlNmVJSG5ZQS9OMnJndGRCSDVidz09

Meeting ID: 984 3899 0666 Passcode: 085177

Abstract: 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.

Bio: Buket Özkaya received the B.S. degree in mathematics from Boğaziçi University, Istanbul, in 2006, the M.S. degree in mathematics from Georg-August-Universität Göttingen, Germany, in 2009, and the Ph.D. degree from Sabancı University, Istanbul, in 2014, under the supervision of Cem Güneri. She held several post-doctoral positions at Middle East Technical University, Ankara, at Telécom ParisTech, France, at Sabancı University, Istanbul, and at Nanyang Technological University, Singapore. Since 2023, she has been an Assistant Professor at the Institute of Applied Mathematics, Middle East Technical University, Ankara. She is interested in algebraic coding theory and its applications.