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D.10.1 brnoeth_lib

Brill-Noether Algorithm, Weierstrass-SG and AG-codes
Jose Ignacio Farran Martin, ignfar@eis.uva.es
Christoph Lossen, lossen@mathematik.uni-kl.de

Implementation of the Brill-Noether algorithm for solving the Riemann-Roch problem and applications to Algebraic Geometry codes. The computation of Weierstrass semigroups is also implemented.
The procedures are intended only for plane (singular) curves defined over a prime field of positive characteristic.
For more information about the library see the end of the file brnoeth.lib.


D.10.1.1 Adj_div  computes the conductor of a curve
D.10.1.2 NSplaces  computes non-singular places with given degrees
D.10.1.3 BrillNoether  computes a vector space basis of the linear system L(D)
D.10.1.4 Weierstrass  computes the Weierstrass semigroup of C at P up to m
D.10.1.5 extcurve  extends the curve C to an extension of degree d
D.10.1.6 AGcode_L  computes the evaluation AG code with divisors G and D
D.10.1.7 AGcode_Omega  computes the residual AG code with divisors G and D
D.10.1.8 prepSV  preprocessing for the basic decoding algorithm
D.10.1.9 decodeSV  decoding of a word with the basic decoding algorithm
D.10.1.10 closed_points  computes the zero-set of a zero-dim. ideal in 2 vars
D.10.1.11 dual_code  computes the dual code
D.10.1.12 sys_code  computes an equivalent systematic code
D.10.1.13 permute_L  applies a permutation to a list