Linear codes over rings, the McWilliams extension theorem, and various classes of rings

Speaker：Henry Chimal Dzul
Date：Tues. 2021-01-26 11:00
Tencent meeting ID：937 090 332 

Abstract：

The theory of linear codes over finite fields has been generalized to a theory of linear codes over finite rings (not necessarily commutative). In this talk we review the main notions of this new theory and the famous McWilliam Extension Theorem for codes. A classification of finite rings up to isomorphism stands out along the way, which makes a 180 degree turn to understand the theory of finite rings and various of their properties relating zero divisors.

About the speaker：

Mr. Henry Chimal obtained his bachelor's degree in mathematics at the Autonomous University of Yucatan, Mexico, in 2007. He completed his master studies at the Metropolitan Autonomous University in Mexico, where he was awarded with the "Academic Excellence Medal" for his outstanding research in coding theory and obtaining a GPA of 10/10. Currently, he is a Ph.D candidate in Mathematics at Ohio University. His topics of interest include coding theory, cryptography and related areas like algebra, number theory, and symbolic computation.