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.
Falcone, G., Filippone, G. (2024). Mumford representation and Riemann-Roch space of a divisor on a hyperelliptic curve. CRYPTOGRAPHY AND COMMUNICATIONS [10.1007/s12095-024-00713-2].
Mumford representation and Riemann-Roch space of a divisor on a hyperelliptic curve
Falcone, Giovanni;Filippone, Giuseppe
2024-04-10
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.
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