Attaining Sudan's decoding radius with no genus penalty for algebraic geometry codes

Isabella Panaccione (1)

1 GRACE - Geometry, arithmetic, algorithms, codes and encryption

In this paper we present a decoding algorithm for algebraic geometry codes with error-correcting capacity beyond half the designed distance of the code. This algorithm comes as a fusion of the Power Error Locating Pairs algorithm for algebraic geometry codes and the technique used by Ehrhard in order to correct these codes up to half the designed distance. The decoding radius of this algorithm reaches that of Sudan algorithm, without any penalty given by the genus of the curve.

Mots clés: Error correcting codes; algebraic geometry codes; decoding algorithms; error correcting pairs; Sudan algorithm; genus

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

Isabella Panaccione. Attaining Sudan's decoding radius with no genus penalty for algebraic geometry codes. 2021. ⟨hal-03177569v2⟩