Twisting Goppa Codes

Majid Farhadi , Marc Perret (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

The aim of this paper is to explain how, starting from a Goppa code C(X, G, P1, . . . , Pn) and a cyclic covering π : Y → X of degree m, oone can twist the initial code to another one C(X, G + Dχ , P1, . . . , Pn), where Dχ is a non-principal degree 0 divisor on X associated to a character χ of Gal(Y /X), in the hope that X (G + Dχ) > X (G). We give, using a MAGMA program, several examples where this occurs, and where both the initial and twisted codes have same minimum distance, so that initial codes have been improved.

Mots clés: Goppa Codes

Domaines: Théorie des nombres [math.NT]

Majid Farhadi, Marc Perret. Twisting Goppa Codes. Finite Fields and Their Applications, 2008, 14, pp.1091-1100. ⟨hal-00967397⟩