Explicit constructions of NMDS self-dual codes

The article delves into the intricate world of NMDS self-dual codes, a crucial area of coding theory with applications in cryptography and telecommunications. It begins by defining NMDS codes and their relationship with MDS codes, highlighting the need for further study due to their potential in cryptographic systems. The authors introduce a new class of linear codes that are either MDS or NMDS, depending on a specific zero-sum condition. In the case of NMDS codes, they present an effective method to construct NMDS self-dual codes, vastly expanding the known parameters. The paper also explores constructions based on multiplicative and additive subgroups, providing a comprehensive approach to understanding and utilizing these codes. The research not only contributes to the theoretical foundation of coding theory but also offers practical applications in secure communication systems.