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.

Falcone G., Figula A., Hannusch C. (2022). On the generating matrices of Goppa codes over hyperelliptic curves. JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 37(3), 273-279.

On the generating matrices of Goppa codes over hyperelliptic curves

Falcone G.
;
2022-01-01

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.
2022
Settore MAT/03 - Geometria
Falcone G., Figula A., Hannusch C. (2022). On the generating matrices of Goppa codes over hyperelliptic curves. JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 37(3), 273-279.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/619320
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