Accessibility setting

Section: New Results

Error Locating pairs

Participants : Alain Couvreur, Isabella Panaccione.

Algebraic codes such as Reed–Solomon codes and algebraic geometry codes benefit from efficient decoding algorithms permitting to correct errors up to half the minimum distance and sometimes beyond. In 1992, Pellikaan proved that many unique decoding could be unified using an object called Error correcting pair. In short, given an error correcting code $𝒞$, an error correcting pair for $𝒞$ is a pair of codes $(𝒜,ℬ)$ whose component wise product $𝒜*ℬ$ is contained in the dual code ${𝒞}^{\perp }$ and such that $𝒜,ℬ$ satisfy some constraints of dimension and minimum distance.

On the other hand, in the late 90's, after the breakthrough of Sudan and Guruswami Sudan the question of list decoding permitting to decode beyond half the minimum distance. In a recently submitted article, A. Couvreur and I. Panaccione [15] proposed a unified point of view for probabilistic decoding algorithms decoding beyond half the minimum distance. Similarly to Pellikaan's result, this framework applies to any code benefiting from an error locating pair which is a relaxed version of error correcting pairs.