A characterization of MDS codes that have an error correcting pair

Irene Márquez-Corbella (1) , Ruud Pellikaan (2)

1 SECRET - Security, Cryptology and Transmissions
2 Department of mathematics and computing science [Eindhoven]

Error-correcting pairs (ECP) were introduced as a general algebraic method of decoding linear codes. These pairs exist for several classes of codes such as for generalized Reed-Solomon, cyclic, alternant and algebraic geometry codes. However little or no study has been made for characterizing those codes. This article is an attempt to fill the vacuum left by the literature concerning this subject. The aim of this paper is to characterize those t-error correcting MDS codes that have a t-error correcting pair.

Domaines: Géométrie algébrique [math.AG]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Irene Márquez-Corbella, Ruud Pellikaan. A characterization of MDS codes that have an error correcting pair. Applications of Computer Algebra ACA 2015, Jul 2015, Kalamata, Greece. ⟨hal-01243392⟩