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

Abstract

AbstractFor an (imaginary) hyperelliptic curve $$\mathcal {H}$$ H of genus g, with a Weierstrass point $$\Omega $$ Ω , taken as the point at infinity, we determine a basis of the Riemann-Roch space $$\mathcal {L}(\Delta + m \Omega )$$ L ( Δ + m Ω ) , where $$\Delta $$ Δ is of degree zero, directly from the Mumford representation of $$\Delta $$ Δ . This provides in turn a generating matrix of a Goppa code.