Explicit bases of the Riemann-Roch spaces on divisors on hyperelliptic curves

12/16/2020

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by   Giovanni Falcone, et al.

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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. As an application, we determine a generator matrix of a Goppa code for j=g=3 and n=4.