Section: New Results

Reed–Solomon-Gabidulin Codes

Participant : Xavier Caruso.

In [31], X. Caruso and A. Durand define a new family of linear codes which is a common generalization of Reed–Solomon codes on the one hand and Gabidulin codes on the other hand. Their construction works over an arbitrary field (not necessarily finite) equipped with an automorphism of finite order and a twisted derivation whose subfield of constants is sufficiently large. This setting allows for example the base field to be ${𝔽}_q\left(t\right)$ equipped with its natural derivation and then provides a new large family of interesting codes. Caruso and Durand then compute the minimal distance of their codes and design an efficient algorithm for decoding up to the half of the minimal distance.