Introduction to Algebraic Coding Theory: alphabets, constacyclic codes, applications, and generalizations

Thời gian: 14:00 đến 16:00 Ngày 23/05/2022

Địa điểm: C101, VIASM

Báo cáo viên: Dinh Quang Hai

Tóm tắt:

The existence of noise in communication channels is an unavoidable fact of life.  The common feature of communication channels is that the original information is sent across a noisy channel to a receiver at the other end, where the received message is not always the same as what was sent. The fundamental problem is to detect if there is an error, and in such case, to determine what message was sent based on the approximation that was received. A response to this problem has been the creation of error-correcting codes. Coding Theory has grown into an important subject that intersects various scientific disciplines, such as information theory, electrical engineering, mathematics, physics, biology, and computer science, for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the detection and correction of errors in the transmitted data. In this talk, we will discuss the historical background of Algebraic Coding Theory, and how beginners can start doing research in Coding Theory by studying the algebraic structure of the so-called constacyclic codes. We will introduce basic properties of such codes, and their structures, applications, as well as possible generalizations.