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D.10.1.8 prepSV

Procedure from library brnoeth.lib (see brnoeth_lib).

Usage:
prepSV( G, D, F, EC ); G,D,F intvecs and EC a list

Return:
list E of size n+3, where n=size(D). All its entries but E[n+3] are matrices:
 
   E[1]:  parity check matrix for the current AG code
   E[2] ... E[n+2]:  matrices used in the procedure decodeSV
   E[n+3]:  intvec with
       E[n+3][1]: correction capacity 
 of the algorithm
       E[n+3][2]: designed Goppa distance 
 of the current AG code

Note:
Computes the preprocessing for the basic (Skorobogatov-Vladut) decoding algorithm.
The procedure must be called within the ring EC[1][4], where EC is the output of extcurve(d) (or in the ring EC[1][2] if d=1)
The intvec G and F represent rational divisors (see BrillNoether for more details).
The intvec D refers to rational places (see AGcode_Omega for more details.). The current AG code is AGcode_Omega(G,D,EC).
If you know the exact minimum distance d and you want to use it in decodeSV instead of , you can change the value of E[n+3][2] to d before applying decodeSV.
If you have a systematic encoding for the current code and want to keep it during the decoding, you must previously permute D (using permute_L(D,P);), e.g., according to the permutation P=L[3], L being the output of sys_code.

Warnings:
F must be a divisor with support disjoint from the support of D and with degree , where

.
G should satisfy , which is not checked by the algorithm.
G and D should also have disjoint supports (checked by the algorithm).

Example:
 
See also: AGcode_Omega; decodeSV; extcurve; permute_L; sys_code.


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            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.