D.9.1 brnoeth_lib

Library:

brnoeth.lib

Purpose:

Brill-Noether Algorithm, Weierstrass-SG and AG-codes

Authors:

Jose Ignacio Farran Martin, ignfar@eis.uva.es
Christoph Lossen, lossen@mathematik.uni-kl.de

Overview:

Implementation of the Brill-Noether algorithm for solving the Riemann-Roch problem and applications in 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.

Main procedures:

D.9.1.1 Adj_div		computes the conductor of a curve
D.9.1.2 NSplaces		computes non-singular places with given degrees
D.9.1.3 BrillNoether		computes a vector space basis of the linear system L(D)
D.9.1.4 Weierstrass		computes the Weierstrass semigroup of C at P up to m
D.9.1.5 extcurve		extends the curve C to an extension of degree d
D.9.1.6 AGcode_L		computes the evaluation AG code with divisors G and D
D.9.1.7 AGcode_Omega		computes the residual AG code with divisors G and D
D.9.1.8 prepSV		preprocessing for the basic decoding algorithm
D.9.1.9 decodeSV		decoding of a word with the basic decoding algorithm

Auxiliary procedures:

D.9.1.10 closed_points		computes the zero-set of a zero-dim. ideal in 2 vars
D.9.1.11 dual_code		computes the dual code
D.9.1.12 sys_code		computes an equivalent systematic code
D.9.1.13 permute_L		applies a permutation to a list

See also: hnoether_lib; triang_lib.