Advances in Coding Theory

The field of coding theory is moving towards the development of more efficient and reliable codes, with a focus on maximizing recoverability and minimizing storage overhead. Researchers are exploring new constructions and characterizations of codes, such as maximally recoverable codes with locality and availability, and irredundant orthogonal arrays. These advances have the potential to improve data storage and communication systems. Notably, new constructions of additive codes from linear codes and generalized Roth-Lempel linear codes are being investigated, and bounds on the minimum distance and covering radius of irredundant orthogonal arrays are being established. Some noteworthy papers include: the introduction of maximally recoverable codes with locality and availability, which enables reduced storage overhead for the same locality and availability, and the construction of new families of linear irredundant orthogonal arrays based on self-dual, Maximum Distance Separable, and MDS-self-dual codes.

Sources

Maximally recoverable codes with locality and availability

On irredundant orthogonal arrays

Additive codes from linear codes

The equivalent condition for GRL codes to be MDS, AMDS or self-dual

Some constructions of non-generalized Reed-Solomon MDS Codes

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