Home Online Manual
Back: prepSV
Forward: closed_points
FastBack: Visualization
FastForward: decodegb_lib
Up: brnoeth_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.10.1.9 decodeSV

Procedure from library brnoeth.lib (see brnoeth_lib).

decodeSV( y, K ); y a row-matrix and K a list

a codeword (row-matrix) if possible, resp. the 0-matrix (of size 1) if decoding is impossible.
For decoding the basic (Skorobogatov-Vladut) decoding algorithm is applied.

The list_expression should be the output K of the procedure prepSV.
The matrix_expression should be a (1 x n)-matrix, where n = ncols(K[1]).
The decoding may fail if the number of errors is greater than the correction capacity of the algorithm.

LIB "brnoeth.lib";
int plevel=printlevel;
ring s=2,(x,y),lp;
list HC=Adj_div(x3+y2+y);
==> The genus of the curve is 1
==> Total number of rational places : NrRatPl = 9
def ER=HC[1][4];
setring ER;
intvec G=5;      // the rational divisor G = 5*HC[3][1]
intvec D=2..9;   // D = sum of the rational places no. 2..9 over F_4
// construct the corresp. residual AG code of type [8,3,>=5] over F_4:
matrix C=AGcode_Omega(G,D,HC);
==> Vector basis successfully computed 
// we can correct 1 error and the genus is 1, thus F must have degree 2
// and support disjoint from that of D
intvec F=2;
list SV=prepSV(G,D,F,HC);
==> Vector basis successfully computed 
==> Vector basis successfully computed 
==> Vector basis successfully computed 
// now we produce 1 error on the zero-codeword :
matrix y[1][8];
// and then we decode :
==> 0,0,0,0,0,0,0,0
See also: AGcode_Omega; extcurve; prepSV.