Manh Thang Vo
Ohio University
Title
A Novel Non-Commutative Ring Whose Ideals are Quasi-Cyclic Codes
Abstract
Quasi-cyclic (QC) codes have been the subject of active research for more than 60 years. In this talk, we introduce a novel family of noncommutative rings whose left and right ideals naturally yield QC codes. Building upon the concepts of m-nomial and entangled polynomials recently introduced by López-Permouth and Pallone, we construct this new family by creating an entangled environment for cosets of polynomials, a concept we refer to as "entangled pods."
Furthermore, we show that the codes generated in this fashion satisfy a stronger, highly structured requirement, which we formally define as being left (right) shuffle-cyclic. We also explore how this same algebraic object can be viewed as a module in various ways, noting that in each of these cases, the corresponding submodules also form QC codes.
This presentation is based on joint work with Sergio López-Permouth.
Zoom Link: https://osu.zoom.us/j/91349080594?pwd=avXqSsCgQuSTmtTprUm2nJERrfbgiK.1