The theta divisor of a jacobian variety and the decoding of geometric Goppa codes Original Research Article

Pellikaan (1989) has given a noneffective maximal decoding algorithm of a geometric code. To this end, our purpose is the determination of the minimal integer s, such that the maps Ψsg − k (k = 1,2), defined in Pellikaan (1989), are surjective. Then, on the one hand, we show that the theta divisor of the jacobian variety of an algebraic curve provides partial answers. On the other hand, for the Klein quartic defined over F8, we determine explicitly divisors of degree 8 which allows us to decode up to 5 errors.