Constacyclic codes over finite fields and finite chain rings and their applications

Thời gian: 14:00 đến 16:00 Ngày 03/06/2022

Địa điểm: C101, VIASM

Báo cáo viên: Nguyen Trong Bac, Dinh Quang Hai

Tóm tắt:

Noise is unavoidable. You cannot get rid of it; all you can do is manage it. Codes are used for data compression, cryptography, error-correction, and more recently for network coding. The study of codes has grown into an important subject that lies at the intersection of various disciplines, including information theory, electrical engineering, mathematics, and computer science. Its purpose is designing efficient, reliable, and secure data transmission methods. The expression `algebraic coding theory' refers to the approach to coding theory where alphabets and ambients are enhanced with algebraic structures to facilitate the design, analysis, and decoding of the codes produced. As with coding theory in general, algebraic coding theory is divided in two major subcategories of study: block codes and convolutional codes. The study of block codes focuses on three important parameters: code length, total number of codewords, and minimum distance between codewords. Originally, work centered on the Hamming distance. Recently, fueled by an incremental use of finite rings as alphabets, the use of other distances such as the Lee distance, the uniform distance, and Euclidean distance has increased. The algebraic theory of error-correcting codes has traditionally taken place in the setting of vector spaces over finite fields. Codes over finite rings were first considered in the early 1970s. But they might have initially been considered mostly as a mathematical curiosity and their study was limited to only a handful of publications. In this talk, we will discuss constacyclic codes over finite fields and finite chain rings and their applications.