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D.10.2.18 decodeRandomFL

Procedure from library decodegb.lib (see decodegb_lib).

Usage:
decodeRandomFL(redun,p,e,n,t,ncodes,ntrials,minpol);
 
          - n is length of codes generated,
          - redun = redundancy of codes generated,
          - p is the characteristic,
          - e is the extension degree,
          - t is the number of errors to correct,
          - ncodes is the number of random codes to be processed,
          - ntrials is the number of received vectors per code to be corrected,
          - minpol: due to some pecularities of SINGULAR one needs to provide
          minimal polynomial for the extension explicitly

Return:
nothing

Example:
 
LIB "decodegb.lib";
// correcting one error for one random binary code of length 25,
// redundancy 14; 10 words are processed
decodeRandomFL(25,14,2,1,1,1,10,"");
==> Codeword:
==> 1,0,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,1,1,0
==> Received word
==> 1,0,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,1,1,0
==> Groebner basis of the FL system:
==> x1(1)+1,
==> x1(2),
==> x1(3),
==> x1(4),
==> x1(5)+1,
==> e(1)+1
==> Codeword:
==> 1,0,0,1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0
==> Received word
==> 1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,1,1,1,1,0,0,0
==> Groebner basis of the FL system:
==> x1(1),
==> x1(2)+1,
==> x1(3)+1,
==> x1(4),
==> x1(5),
==> e(1)+1
==> Codeword:
==> 0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0
==> Received word
==> 0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0
==> Groebner basis of the FL system:
==> x1(1),
==> x1(2)+1,
==> x1(3),
==> x1(4),
==> x1(5),
==> e(1)+1
==> Codeword:
==> 0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,1
==> Received word
==> 0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,1
==> Groebner basis of the FL system:
==> x1(1),
==> x1(2),
==> x1(3)+1,
==> x1(4),
==> x1(5),
==> e(1)+1
==> Codeword:
==> 1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,1
==> Received word
==> 1,1,0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0,1,1,0,1,1,1
==> Groebner basis of the FL system:
==> x1(1),
==> x1(2)+1,
==> x1(3)+1,
==> x1(4),
==> x1(5)+1,
==> e(1)+1
==> Codeword:
==> 0,1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0
==> Received word
==> 0,1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0
==> Groebner basis of the FL system:
==> x1(1)+1,
==> x1(2),
==> x1(3)+1,
==> x1(4),
==> x1(5),
==> e(1)+1
==> Codeword:
==> 1,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0,0,1,1
==> Received word
==> 1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,1,0,0,1,1
==> Groebner basis of the FL system:
==> x1(1),
==> x1(2),
==> x1(3)+1,
==> x1(4)+1,
==> x1(5)+1,
==> e(1)+1
==> Codeword:
==> 0,1,0,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1,1
==> Received word
==> 0,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1,1
==> Groebner basis of the FL system:
==> x1(1),
==> x1(2)+1,
==> x1(3),
==> x1(4),
==> x1(5),
==> e(1)+1
==> Codeword:
==> 0,1,0,0,1,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,1
==> Received word
==> 0,1,0,0,1,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0
==> Groebner basis of the FL system:
==> x1(1)+1,
==> x1(2)+1,
==> x1(3),
==> x1(4),
==> x1(5),
==> e(1)+1
==> Codeword:
==> 1,0,0,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1
==> Received word
==> 1,0,0,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,1,1
==> Groebner basis of the FL system:
==> x1(1)+1,
==> x1(2),
==> x1(3)+1,
==> x1(4),
==> x1(5)+1,
==> e(1)+1