MDS Self-dual Codes: Existence and Constructions

Speaker: Professor Keqin Feng,  Tsinghua University, Beijing

Time: 9:30-11:30， March 29, Friday, 2019

Venue: 200-9, Sir Run Run Shaw Business Building

Abstract:   MDS linear codes [n,k,d} over Fq ( d=n-k+1) and self-dual codes are hot topics in coding theory  for years since they have theoretical interests and closed relations with other mathematical disciplins ( finite geometry, association schemes, modular forms,lattices, group theory, combinatorial designs,...) and have applications in communication and cryptography. In past 2-3 years, several papers appeared to deal with MDS self-dual codes ( so that n=2k and d=k+1) . The basic problem is that which n can be the length of  such codes over Fq and how to construct them? In this talk we will show  a unified approach to summary most of  known results firstly, then show several new constructions on such codes by using our approach, give some non-existence results and raise some open problems.