On the generating matrices of Goppa codes over hyperelliptic curves

Abstract

For an (imaginary) hyperelliptic curve H of genus g, we determine a basis of the Riemann-Roch space L(D), where D is a divisor with positive degree n, linearly equivalent to P{1} + … + P{j} + (n − j)Ω, with 0 ≤ j ≤ g, where Ω is a Weierstrass point, taken as the point at infinity. Directly, this provides in turn a generating matrix of a Goppa codes.