Mumford representation and Riemann-Roch space of a divisor on a hyperelliptic curve

Abstract

For an (imaginary) hyperelliptic curve H of genus g, with a Weierstrass point O, taken as the point at infinity, we determine a basis of the Riemann-Roch space L( D + mO), where D is of degree zero, directly from the Mumford representation of D. This provides in turn a generating matrix of a Goppa code.