### D.10.1 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 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.

Procedures:

> 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

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