# Singular

#### 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 ```