##
##
##  Decodes the Golay 12,6,6 code using S(5,6,12)
##         and the MINIMOG
##
##        This package uses GUAVA
##
##   Example commands to start using this program:
##
##LogTo("/home/wdj/gapstuff/hexads.log"); #for unix
##LogTo("c:/gap/logfiles/hexads.log");    #for windows
##RequirePackage("guava");
##Read("/home/wdj/gapstuff/golay12.g");   #for unix
##Read("c:/gap/gapfiles/golay12.g");      #for windows
##
##wdj,12-2001
######################################################3
##
##                  The Golay code 12,6,6
##
#r1 :=[0, 0, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0];;
#r2 :=[0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1];;
#r3 :=[0, 2, 2, 0, 1, 0, 0, 1, 1, 0, 0, 1];;
#r4 :=[0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1];;
#r5 :=[0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1];;
#r6 :=[1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 1];;
#G:=[r1,r2,r3,r4,r5,r6];;
#C12:=GeneratorMatCode(G,GF(3));;
#wt6_codewords_wt( C12, 6);;
#wt9_codewords:=codewords_wt( C12, 9);;
#wt12_codewords_wt( C12, 12);;
##
#########################################################
##
##                 Examples
##
## decoding a random wt 12 codeword with 2 errors
##
#c:=Random(wt12_codewords);
#n1:=Random([1..12]);
#n2:=Random([1..12]);
#if n1=n2 and n1<12 then n2:=n1+1; fi;
#if n1=n2 and n1=12 then n2:=n1-1; fi;
#e:=[];
#for i in [1..12] do
# if i in [n1,n2] then e[i]:=1; else e[i]:=0; fi;
#od;
#r:=(e+c) mod 3;
#decode(r);
##
##
## decoding a random wt 9 codeword with 2 errors
##
#c:=Random(wt9_codewords);
#n1:=Random([1..12]);
#n2:=Random([1..12]);
#if n1=n2 and n1<12 then n2:=n1+1; fi;
#if n1=n2 and n1=12 then n2:=n1-1; fi;
#e:=[];
#for i in [1..12] do
# if i in [n1,n2] then e[i]:=1; else e[i]:=0; fi;
#od;
#r:=(e+c) mod 3;
#decode(r);
##
##
## decoding a random wt 6 codeword with 2 errors
##
#c:=Random(wt6_codewords);
#n1:=Random([1..12]);
#n2:=Random([1..12]);
#if n1=n2 and n1<12 then n2:=n1+1; fi;
#if n1=n2 and n1=12 then n2:=n1-1; fi;
#e:=[];
#for i in [1..12] do
# if i in [n1,n2] then e[i]:=1; else e[i]:=0; fi;
#od;
#r:=(e+c) mod 3;
#decode(r);
##
###########################################################

minimog_shuffle:=[[6,3,0,9],[5,2,7,10],[4,1,8,11]];;


#hexads in the S(5,6,12) with shuffle labeling
#obtained from:
#for x in hexad_codewords do Add(S2,support_word(x)); od; S2;
hexads:=[ [ 0, 9, 5, 2, 4, 1 ], [ 0, 9, 7, 10, 8, 11 ], [ 3, 0, 5, 10, 4, 11 ],
  [ 3, 9, 5, 7, 10, 11 ], [ 0, 2, 7, 4, 8, 11 ], [ 6, 0, 5, 10, 8, 11 ],
  [ 3, 9, 5, 2, 1, 8 ], [ 3, 0, 5, 4, 1, 8 ], [ 9, 5, 10, 4, 1, 8 ],
  [ 6, 9, 7, 4, 8, 11 ], [ 6, 0, 9, 2, 7, 4 ], [ 6, 5, 2, 10, 1, 8 ],
  [ 5, 2, 10, 4, 1, 11 ], [ 0, 5, 7, 4, 1, 11 ], [ 6, 9, 5, 7, 10, 8 ],
  [ 6, 0, 9, 5, 7, 11 ], [ 3, 9, 2, 10, 1, 11 ], [ 0, 2, 7, 10, 4, 1 ],
  [ 3, 0, 9, 5, 7, 1 ], [ 0, 9, 2, 10, 4, 11 ], [ 6, 0, 9, 5, 1, 8 ],
  [ 6, 0, 7, 10, 4, 11 ], [ 6, 5, 2, 10, 1, 8 ], [ 6, 9, 5, 2, 4, 8 ],
  [ 0, 5, 7, 10, 1, 8 ], [ 6, 9, 5, 7, 4, 1 ], [ 0, 5, 2, 10, 4, 8 ],
  [ 6, 0, 9, 10, 4, 8 ], [ 6, 9, 2, 7, 10, 11 ], [ 0, 9, 2, 10, 1, 8 ],
  [ 3, 9, 10, 4, 8, 11 ], [ 9, 5, 2, 7, 10, 1 ], [ 6, 0, 9, 2, 7, 4 ],
  [ 6, 3, 0, 9, 5, 4 ], [ 6, 0, 9, 7, 10, 1 ], [ 6, 5, 4, 1, 8, 11 ],
  [ 6, 3, 9, 4, 1, 8 ], [ 3, 9, 5, 2, 10, 4 ], [ 6, 3, 0, 5, 7, 10 ],
  [ 5, 2, 7, 4, 1, 8 ], [ 6, 0, 9, 2, 8, 11 ], [ 3, 9, 5, 2, 10, 4 ],
  [ 0, 9, 7, 4, 1, 8 ], [ 9, 2, 4, 1, 8, 11 ], [ 3, 0, 5, 2, 7, 4 ],
  [ 9, 5, 7, 1, 8, 11 ], [ 6, 5, 7, 10, 1, 11 ], [ 3, 5, 2, 7, 10, 8 ],
  [ 6, 0, 2, 10, 1, 11 ], [ 3, 0, 2, 4, 1, 11 ], [ 6, 3, 10, 4, 1, 11 ],
  [ 3, 0, 9, 10, 4, 1 ], [ 6, 3, 2, 1, 8, 11 ], [ 6, 0, 5, 2, 7, 1 ],
  [ 6, 3, 9, 5, 2, 7 ], [ 0, 9, 2, 10, 4, 11 ], [ 3, 0, 5, 2, 10, 1 ],
  [ 3, 5, 2, 4, 8, 11 ], [ 9, 5, 10, 4, 1, 8 ], [ 6, 3, 0, 9, 2, 1 ],
  [ 9, 5, 2, 7, 4, 11 ], [ 6, 3, 0, 5, 2, 8 ], [ 3, 9, 2, 7, 8, 11 ],
  [ 9, 5, 2, 10, 8, 11 ], [ 6, 0, 5, 10, 4, 1 ], [ 3, 0, 7, 10, 1, 11 ],
  [ 3, 9, 5, 4, 1, 11 ], [ 3, 9, 5, 2, 1, 8 ], [ 3, 2, 7, 10, 4, 11 ],
  [ 0, 5, 2, 7, 10, 11 ], [ 6, 9, 10, 1, 8, 11 ], [ 3, 5, 7, 10, 4, 1 ],
  [ 6, 0, 5, 7, 4, 8 ], [ 3, 5, 2, 7, 10, 8 ], [ 0, 10, 4, 1, 8, 11 ],
  [ 6, 3, 9, 7, 10, 4 ], [ 6, 3, 0, 4, 8, 11 ], [ 6, 0, 2, 4, 1, 8 ],
  [ 6, 7, 10, 4, 1, 8 ], [ 6, 3, 2, 7, 4, 8 ], [ 3, 0, 2, 4, 1, 11 ],
  [ 6, 3, 9, 5, 10, 1 ], [ 3, 7, 4, 1, 8, 11 ], [ 6, 9, 5, 2, 1, 11 ],
  [ 6, 9, 2, 7, 1, 8 ], [ 3, 0, 7, 10, 4, 8 ], [ 6, 3, 0, 9, 10, 11 ],
  [ 6, 5, 2, 7, 10, 4 ], [ 6, 3, 0, 5, 1, 11 ], [ 0, 9, 5, 2, 4, 1 ],
  [ 0, 5, 7, 4, 1, 11 ], [ 6, 5, 2, 7, 8, 11 ], [ 6, 0, 9, 2, 8, 11 ],
  [ 3, 9, 5, 4, 1, 11 ], [ 6, 3, 0, 2, 10, 4 ], [ 6, 3, 0, 10, 1, 8 ],
  [ 3, 5, 10, 1, 8, 11 ], [ 6, 0, 9, 5, 2, 10 ], [ 6, 0, 2, 4, 1, 8 ],
  [ 6, 3, 9, 7, 1, 11 ], [ 0, 2, 7, 10, 4, 1 ], [ 6, 3, 2, 7, 4, 8 ],
  [ 6, 3, 5, 7, 1, 8 ], [ 6, 3, 5, 10, 4, 8 ], [ 9, 5, 2, 7, 10, 1 ],
  [ 3, 0, 2, 7, 1, 8 ], [ 6, 3, 9, 5, 10, 1 ], [ 3, 9, 2, 7, 4, 1 ],
  [ 3, 0, 9, 7, 4, 11 ], [ 3, 0, 7, 10, 4, 8 ], [ 5, 2, 7, 4, 1, 8 ],
  [ 3, 0, 5, 2, 7, 4 ], [ 6, 9, 5, 10, 4, 11 ], [ 3, 9, 2, 7, 4, 1 ],
  [ 3, 9, 5, 7, 4, 8 ], [ 3, 2, 7, 10, 4, 11 ], [ 6, 3, 0, 9, 2, 1 ],
  [ 6, 3, 5, 2, 10, 11 ], [ 3, 5, 2, 7, 1, 11 ], [ 6, 0, 7, 1, 8, 11 ],
  [ 6, 3, 9, 7, 1, 11 ], [ 6, 9, 2, 10, 4, 1 ], [ 0, 9, 5, 10, 1, 11 ],
  [ 6, 3, 5, 2, 4, 1 ], [ 6, 3, 9, 7, 10, 4 ], [ 6, 0, 9, 4, 1, 11 ],
  [ 6, 9, 5, 2, 4, 8 ], [ 6, 3, 10, 4, 1, 11 ], [ 6, 0, 5, 2, 7, 1 ],
  [ 3, 5, 2, 4, 8, 11 ], [ 6, 9, 2, 7, 10, 11 ], [ 3, 0, 2, 10, 8, 11 ],
  [ 6, 2, 10, 4, 8, 11 ], [ 9, 5, 7, 1, 8, 11 ], [ 6, 0, 2, 7, 10, 8 ],
  [ 9, 2, 7, 10, 4, 8 ], [ 6, 3, 0, 5, 2, 8 ], [ 3, 0, 9, 1, 8, 11 ],
  [ 9, 5, 2, 10, 8, 11 ], [ 6, 0, 5, 2, 4, 11 ], [ 0, 5, 2, 1, 8, 11 ],
  [ 6, 3, 0, 5, 7, 10 ], [ 6, 3, 0, 7, 4, 1 ], [ 3, 0, 5, 4, 1, 8 ],
  [ 6, 3, 9, 2, 10, 8 ], [ 6, 3, 9, 4, 1, 8 ], [ 3, 9, 2, 10, 1, 11 ],
  [ 3, 0, 9, 2, 4, 8 ], [ 3, 9, 2, 7, 8, 11 ], [ 6, 9, 7, 4, 8, 11 ],
  [ 3, 0, 9, 1, 8, 11 ], [ 0, 2, 7, 4, 8, 11 ], [ 6, 5, 4, 1, 8, 11 ],
  [ 0, 9, 5, 2, 7, 8 ], [ 6, 3, 2, 7, 10, 1 ], [ 6, 3, 9, 2, 4, 11 ],
  [ 6, 0, 5, 2, 4, 11 ], [ 6, 3, 9, 5, 2, 7 ], [ 3, 0, 2, 7, 1, 8 ],
  [ 6, 0, 9, 5, 1, 8 ], [ 6, 0, 7, 10, 4, 11 ], [ 6, 3, 0, 10, 1, 8 ],
  [ 6, 3, 7, 10, 8, 11 ], [ 6, 3, 0, 9, 7, 8 ], [ 6, 3, 0, 4, 8, 11 ],
  [ 0, 5, 2, 10, 4, 8 ], [ 3, 5, 7, 10, 4, 1 ], [ 0, 9, 5, 7, 10, 4 ],
  [ 6, 2, 7, 4, 1, 11 ], [ 2, 7, 10, 1, 8, 11 ], [ 6, 3, 5, 10, 4, 8 ],
  [ 6, 3, 0, 7, 4, 1 ], [ 3, 5, 2, 7, 1, 11 ], [ 0, 5, 2, 1, 8, 11 ],
  [ 6, 0, 9, 10, 4, 8 ], [ 3, 0, 5, 7, 8, 11 ], [ 9, 7, 10, 4, 1, 11 ],
  [ 3, 0, 9, 5, 2, 11 ], [ 0, 9, 5, 4, 8, 11 ], [ 3, 0, 9, 10, 4, 1 ],
  [ 2, 7, 10, 1, 8, 11 ], [ 0, 9, 7, 10, 8, 11 ], [ 3, 0, 9, 5, 7, 1 ],
  [ 9, 7, 10, 4, 1, 11 ], [ 3, 0, 9, 5, 2, 11 ], [ 5, 7, 10, 4, 8, 11 ],
  [ 6, 0, 2, 10, 1, 11 ], [ 6, 3, 0, 9, 5, 4 ], [ 3, 7, 4, 1, 8, 11 ],
  [ 0, 9, 5, 10, 1, 11 ], [ 6, 9, 10, 1, 8, 11 ], [ 0, 5, 2, 7, 10, 11 ],
  [ 6, 3, 2, 7, 10, 1 ], [ 3, 9, 10, 4, 8, 11 ], [ 0, 9, 5, 7, 10, 4 ],
  [ 6, 3, 5, 7, 4, 11 ], [ 9, 2, 7, 10, 4, 8 ], [ 6, 3, 7, 10, 8, 11 ],
  [ 3, 0, 2, 10, 8, 11 ], [ 6, 9, 2, 7, 1, 8 ], [ 6, 3, 9, 2, 10, 8 ],
  [ 3, 5, 10, 1, 8, 11 ], [ 0, 9, 2, 7, 1, 11 ], [ 6, 3, 0, 2, 7, 11 ],
  [ 6, 0, 5, 10, 8, 11 ], [ 6, 0, 5, 7, 4, 8 ], [ 6, 3, 9, 5, 8, 11 ],
  [ 0, 5, 7, 10, 1, 8 ], [ 6, 9, 5, 7, 4, 1 ], [ 9, 2, 4, 1, 8, 11 ],
  [ 0, 9, 5, 2, 7, 8 ], [ 6, 3, 5, 2, 4, 1 ], [ 6, 9, 5, 7, 10, 8 ],
  [ 6, 2, 10, 4, 8, 11 ], [ 6, 5, 7, 10, 1, 11 ], [ 6, 2, 7, 4, 1, 11 ],
  [ 3, 0, 9, 7, 4, 11 ], [ 0, 9, 5, 4, 8, 11 ], [ 3, 9, 7, 10, 1, 8 ],
  [ 3, 0, 9, 2, 7, 10 ], [ 6, 0, 9, 5, 7, 11 ], [ 6, 0, 9, 5, 2, 10 ],
  [ 3, 0, 5, 2, 10, 1 ], [ 6, 3, 0, 5, 1, 11 ], [ 9, 5, 2, 7, 4, 11 ],
  [ 3, 0, 5, 10, 4, 11 ], [ 6, 0, 9, 4, 1, 11 ], [ 5, 7, 10, 4, 8, 11 ],
  [ 6, 3, 5, 7, 4, 11 ], [ 6, 0, 7, 1, 8, 11 ], [ 6, 0, 2, 7, 10, 8 ],
  [ 3, 2, 10, 4, 1, 8 ], [ 0, 10, 4, 1, 8, 11 ], [ 0, 9, 7, 4, 1, 8 ],
  [ 6, 3, 0, 9, 7, 8 ], [ 6, 5, 2, 7, 8, 11 ], [ 3, 9, 7, 10, 1, 8 ],
  [ 6, 9, 2, 10, 4, 1 ], [ 5, 2, 10, 4, 1, 11 ], [ 6, 5, 2, 7, 10, 4 ],
  [ 6, 9, 5, 10, 4, 11 ], [ 3, 0, 9, 5, 10, 8 ], [ 3, 2, 10, 4, 1, 8 ],
  [ 3, 0, 9, 2, 7, 10 ], [ 6, 9, 5, 2, 1, 11 ], [ 3, 0, 7, 10, 1, 11 ],
  [ 6, 3, 5, 2, 10, 11 ], [ 6, 3, 5, 7, 1, 8 ], [ 0, 9, 2, 7, 1, 11 ],
  [ 0, 9, 2, 10, 1, 8 ], [ 3, 9, 5, 7, 10, 11 ], [ 3, 9, 5, 7, 4, 8 ],
  [ 6, 3, 9, 5, 8, 11 ], [ 6, 3, 2, 1, 8, 11 ], [ 3, 0, 5, 7, 8, 11 ],
  [ 6, 7, 10, 4, 1, 8 ], [ 6, 0, 5, 10, 4, 1 ], [ 6, 3, 0, 2, 7, 11 ],
  [ 3, 0, 9, 2, 4, 8 ], [ 6, 3, 0, 2, 10, 4 ], [ 6, 3, 0, 9, 10, 11 ],
  [ 6, 0, 9, 7, 10, 1 ], [ 6, 3, 9, 2, 4, 11 ], [ 3, 0, 9, 5, 10, 8 ],
  [ 0, 1, 2, 4, 5, 9 ], [ 0, 7, 8, 9, 10, 11 ], [ 0, 3, 4, 5, 10, 11 ],
  [ 3, 5, 7, 9, 10, 11 ], [ 0, 2, 4, 7, 8, 11 ], [ 0, 5, 6, 8, 10, 11 ],
  [ 1, 2, 3, 5, 8, 9 ], [ 0, 1, 3, 4, 5, 8 ], [ 1, 4, 5, 8, 9, 10 ],
  [ 4, 6, 7, 8, 9, 11 ], [ 0, 2, 4, 6, 7, 9 ], [ 1, 2, 5, 6, 8, 10 ],
  [ 1, 2, 4, 5, 10, 11 ], [ 0, 1, 4, 5, 7, 11 ], [ 5, 6, 7, 8, 9, 10 ],
  [ 0, 5, 6, 7, 9, 11 ], [ 1, 2, 3, 9, 10, 11 ], [ 0, 1, 2, 4, 7, 10 ],
  [ 0, 1, 3, 5, 7, 9 ], [ 0, 2, 4, 9, 10, 11 ], [ 0, 1, 5, 6, 8, 9 ],
  [ 0, 4, 6, 7, 10, 11 ], [ 1, 2, 5, 6, 8, 10 ], [ 2, 4, 5, 6, 8, 9 ],
  [ 0, 1, 5, 7, 8, 10 ], [ 1, 4, 5, 6, 7, 9 ], [ 0, 2, 4, 5, 8, 10 ],
  [ 0, 4, 6, 8, 9, 10 ], [ 2, 6, 7, 9, 10, 11 ], [ 0, 1, 2, 8, 9, 10 ],
  [ 3, 4, 8, 9, 10, 11 ], [ 1, 2, 5, 7, 9, 10 ], [ 0, 2, 4, 6, 7, 9 ],
  [ 0, 3, 4, 5, 6, 9 ], [ 0, 1, 6, 7, 9, 10 ], [ 1, 4, 5, 6, 8, 11 ],
  [ 1, 3, 4, 6, 8, 9 ], [ 2, 3, 4, 5, 9, 10 ], [ 0, 3, 5, 6, 7, 10 ],
  [ 1, 2, 4, 5, 7, 8 ], [ 0, 2, 6, 8, 9, 11 ], [ 2, 3, 4, 5, 9, 10 ],
  [ 0, 1, 4, 7, 8, 9 ], [ 1, 2, 4, 8, 9, 11 ], [ 0, 2, 3, 4, 5, 7 ],
  [ 1, 5, 7, 8, 9, 11 ], [ 1, 5, 6, 7, 10, 11 ], [ 2, 3, 5, 7, 8, 10 ],
  [ 0, 1, 2, 6, 10, 11 ], [ 0, 1, 2, 3, 4, 11 ], [ 1, 3, 4, 6, 10, 11 ],
  [ 0, 1, 3, 4, 9, 10 ], [ 1, 2, 3, 6, 8, 11 ], [ 0, 1, 2, 5, 6, 7 ],
  [ 2, 3, 5, 6, 7, 9 ], [ 0, 2, 4, 9, 10, 11 ], [ 0, 1, 2, 3, 5, 10 ],
  [ 2, 3, 4, 5, 8, 11 ], [ 1, 4, 5, 8, 9, 10 ], [ 0, 1, 2, 3, 6, 9 ],
  [ 2, 4, 5, 7, 9, 11 ], [ 0, 2, 3, 5, 6, 8 ], [ 2, 3, 7, 8, 9, 11 ],
  [ 2, 5, 8, 9, 10, 11 ], [ 0, 1, 4, 5, 6, 10 ], [ 0, 1, 3, 7, 10, 11 ],
  [ 1, 3, 4, 5, 9, 11 ], [ 1, 2, 3, 5, 8, 9 ], [ 2, 3, 4, 7, 10, 11 ],
  [ 0, 2, 5, 7, 10, 11 ], [ 1, 6, 8, 9, 10, 11 ], [ 1, 3, 4, 5, 7, 10 ],
  [ 0, 4, 5, 6, 7, 8 ], [ 2, 3, 5, 7, 8, 10 ], [ 0, 1, 4, 8, 10, 11 ],
  [ 3, 4, 6, 7, 9, 10 ], [ 0, 3, 4, 6, 8, 11 ], [ 0, 1, 2, 4, 6, 8 ],
  [ 1, 4, 6, 7, 8, 10 ], [ 2, 3, 4, 6, 7, 8 ], [ 0, 1, 2, 3, 4, 11 ],
  [ 1, 3, 5, 6, 9, 10 ], [ 1, 3, 4, 7, 8, 11 ], [ 1, 2, 5, 6, 9, 11 ],
  [ 1, 2, 6, 7, 8, 9 ], [ 0, 3, 4, 7, 8, 10 ], [ 0, 3, 6, 9, 10, 11 ],
  [ 2, 4, 5, 6, 7, 10 ], [ 0, 1, 3, 5, 6, 11 ], [ 0, 1, 2, 4, 5, 9 ],
  [ 0, 1, 4, 5, 7, 11 ], [ 2, 5, 6, 7, 8, 11 ], [ 0, 2, 6, 8, 9, 11 ],
  [ 1, 3, 4, 5, 9, 11 ], [ 0, 2, 3, 4, 6, 10 ], [ 0, 1, 3, 6, 8, 10 ],
  [ 1, 3, 5, 8, 10, 11 ], [ 0, 2, 5, 6, 9, 10 ], [ 0, 1, 2, 4, 6, 8 ],
  [ 1, 3, 6, 7, 9, 11 ], [ 0, 1, 2, 4, 7, 10 ], [ 2, 3, 4, 6, 7, 8 ],
  [ 1, 3, 5, 6, 7, 8 ], [ 3, 4, 5, 6, 8, 10 ], [ 1, 2, 5, 7, 9, 10 ],
  [ 0, 1, 2, 3, 7, 8 ], [ 1, 3, 5, 6, 9, 10 ], [ 1, 2, 3, 4, 7, 9 ],
  [ 0, 3, 4, 7, 9, 11 ], [ 0, 3, 4, 7, 8, 10 ], [ 1, 2, 4, 5, 7, 8 ],
  [ 0, 2, 3, 4, 5, 7 ], [ 4, 5, 6, 9, 10, 11 ], [ 1, 2, 3, 4, 7, 9 ],
  [ 3, 4, 5, 7, 8, 9 ], [ 2, 3, 4, 7, 10, 11 ], [ 0, 1, 2, 3, 6, 9 ],
  [ 2, 3, 5, 6, 10, 11 ], [ 1, 2, 3, 5, 7, 11 ], [ 0, 1, 6, 7, 8, 11 ],
  [ 1, 3, 6, 7, 9, 11 ], [ 1, 2, 4, 6, 9, 10 ], [ 0, 1, 5, 9, 10, 11 ],
  [ 1, 2, 3, 4, 5, 6 ], [ 3, 4, 6, 7, 9, 10 ], [ 0, 1, 4, 6, 9, 11 ],
  [ 2, 4, 5, 6, 8, 9 ], [ 1, 3, 4, 6, 10, 11 ], [ 0, 1, 2, 5, 6, 7 ],
  [ 2, 3, 4, 5, 8, 11 ], [ 2, 6, 7, 9, 10, 11 ], [ 0, 2, 3, 8, 10, 11 ],
  [ 2, 4, 6, 8, 10, 11 ], [ 1, 5, 7, 8, 9, 11 ], [ 0, 2, 6, 7, 8, 10 ],
  [ 2, 4, 7, 8, 9, 10 ], [ 0, 2, 3, 5, 6, 8 ], [ 0, 1, 3, 8, 9, 11 ],
  [ 2, 5, 8, 9, 10, 11 ], [ 0, 2, 4, 5, 6, 11 ], [ 0, 1, 2, 5, 8, 11 ],
  [ 0, 3, 5, 6, 7, 10 ], [ 0, 1, 3, 4, 6, 7 ], [ 0, 1, 3, 4, 5, 8 ],
  [ 2, 3, 6, 8, 9, 10 ], [ 1, 3, 4, 6, 8, 9 ], [ 1, 2, 3, 9, 10, 11 ],
  [ 0, 2, 3, 4, 8, 9 ], [ 2, 3, 7, 8, 9, 11 ], [ 4, 6, 7, 8, 9, 11 ],
  [ 0, 1, 3, 8, 9, 11 ], [ 0, 2, 4, 7, 8, 11 ], [ 1, 4, 5, 6, 8, 11 ],
  [ 0, 2, 5, 7, 8, 9 ], [ 1, 2, 3, 6, 7, 10 ], [ 2, 3, 4, 6, 9, 11 ],
  [ 0, 2, 4, 5, 6, 11 ], [ 2, 3, 5, 6, 7, 9 ], [ 0, 1, 2, 3, 7, 8 ],
  [ 0, 1, 5, 6, 8, 9 ], [ 0, 4, 6, 7, 10, 11 ], [ 0, 1, 3, 6, 8, 10 ],
  [ 3, 6, 7, 8, 10, 11 ], [ 0, 3, 6, 7, 8, 9 ], [ 0, 3, 4, 6, 8, 11 ],
  [ 0, 2, 4, 5, 8, 10 ], [ 1, 3, 4, 5, 7, 10 ], [ 0, 4, 5, 7, 9, 10 ],
  [ 1, 2, 4, 6, 7, 11 ], [ 1, 2, 7, 8, 10, 11 ], [ 3, 4, 5, 6, 8, 10 ],
  [ 0, 1, 3, 4, 6, 7 ], [ 1, 2, 3, 5, 7, 11 ], [ 0, 1, 2, 5, 8, 11 ],
  [ 0, 4, 6, 8, 9, 10 ], [ 0, 3, 5, 7, 8, 11 ], [ 1, 4, 7, 9, 10, 11 ],
  [ 0, 2, 3, 5, 9, 11 ], [ 0, 4, 5, 8, 9, 11 ], [ 0, 1, 3, 4, 9, 10 ],
  [ 1, 2, 7, 8, 10, 11 ], [ 0, 7, 8, 9, 10, 11 ], [ 0, 1, 3, 5, 7, 9 ],
  [ 1, 4, 7, 9, 10, 11 ], [ 0, 2, 3, 5, 9, 11 ], [ 4, 5, 7, 8, 10, 11 ],
  [ 0, 1, 2, 6, 10, 11 ], [ 0, 3, 4, 5, 6, 9 ], [ 1, 3, 4, 7, 8, 11 ],
  [ 0, 1, 5, 9, 10, 11 ], [ 1, 6, 8, 9, 10, 11 ], [ 0, 2, 5, 7, 10, 11 ],
  [ 1, 2, 3, 6, 7, 10 ], [ 3, 4, 8, 9, 10, 11 ], [ 0, 4, 5, 7, 9, 10 ],
  [ 3, 4, 5, 6, 7, 11 ], [ 2, 4, 7, 8, 9, 10 ], [ 3, 6, 7, 8, 10, 11 ],
  [ 0, 2, 3, 8, 10, 11 ], [ 1, 2, 6, 7, 8, 9 ], [ 2, 3, 6, 8, 9, 10 ],
  [ 1, 3, 5, 8, 10, 11 ], [ 0, 1, 2, 7, 9, 11 ], [ 0, 2, 3, 6, 7, 11 ],
  [ 0, 5, 6, 8, 10, 11 ], [ 0, 4, 5, 6, 7, 8 ], [ 3, 5, 6, 8, 9, 11 ],
  [ 0, 1, 5, 7, 8, 10 ], [ 1, 4, 5, 6, 7, 9 ], [ 1, 2, 4, 8, 9, 11 ],
  [ 0, 2, 5, 7, 8, 9 ], [ 1, 2, 3, 4, 5, 6 ], [ 5, 6, 7, 8, 9, 10 ],
  [ 2, 4, 6, 8, 10, 11 ], [ 1, 5, 6, 7, 10, 11 ], [ 1, 2, 4, 6, 7, 11 ],
  [ 0, 3, 4, 7, 9, 11 ], [ 0, 4, 5, 8, 9, 11 ], [ 1, 3, 7, 8, 9, 10 ],
  [ 0, 2, 3, 7, 9, 10 ], [ 0, 5, 6, 7, 9, 11 ], [ 0, 2, 5, 6, 9, 10 ],
  [ 0, 1, 2, 3, 5, 10 ], [ 0, 1, 3, 5, 6, 11 ], [ 2, 4, 5, 7, 9, 11 ],
  [ 0, 3, 4, 5, 10, 11 ], [ 0, 1, 4, 6, 9, 11 ], [ 4, 5, 7, 8, 10, 11 ],
  [ 3, 4, 5, 6, 7, 11 ], [ 0, 1, 6, 7, 8, 11 ], [ 0, 2, 6, 7, 8, 10 ],
  [ 1, 2, 3, 4, 8, 10 ], [ 0, 1, 4, 8, 10, 11 ], [ 0, 1, 4, 7, 8, 9 ],
  [ 0, 3, 6, 7, 8, 9 ], [ 2, 5, 6, 7, 8, 11 ], [ 1, 3, 7, 8, 9, 10 ],
  [ 1, 2, 4, 6, 9, 10 ], [ 1, 2, 4, 5, 10, 11 ], [ 2, 4, 5, 6, 7, 10 ],
  [ 4, 5, 6, 9, 10, 11 ], [ 0, 3, 5, 8, 9, 10 ], [ 1, 2, 3, 4, 8, 10 ],
  [ 0, 2, 3, 7, 9, 10 ], [ 1, 2, 5, 6, 9, 11 ], [ 0, 1, 3, 7, 10, 11 ],
  [ 2, 3, 5, 6, 10, 11 ], [ 1, 3, 5, 6, 7, 8 ], [ 0, 1, 2, 7, 9, 11 ],
  [ 0, 1, 2, 8, 9, 10 ], [ 3, 5, 7, 9, 10, 11 ], [ 3, 4, 5, 7, 8, 9 ],
  [ 3, 5, 6, 8, 9, 11 ], [ 1, 2, 3, 6, 8, 11 ], [ 0, 3, 5, 7, 8, 11 ],
  [ 1, 4, 6, 7, 8, 10 ], [ 0, 1, 4, 5, 6, 10 ], [ 0, 2, 3, 6, 7, 11 ],
  [ 0, 2, 3, 4, 8, 9 ], [ 0, 2, 3, 4, 6, 10 ], [ 0, 3, 6, 9, 10, 11 ],
  [ 0, 1, 6, 7, 9, 10 ], [ 2, 3, 4, 6, 9, 11 ], [ 0, 3, 5, 8, 9, 10 ] ];


wt12_codewords:=
[ [ 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2 ], 
[ 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1 ],
  [ 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1 ], 
[ 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2 ],
  [ 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1 ], 
[ 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2 ],
  [ 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1 ], 
[ 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2 ],
  [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
[ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1 ],
  [ 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2 ], 
[ 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 ],
  [ 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2 ], 
[ 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1 ],
  [ 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2 ], 
[ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 ],
  [ 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1 ], 
[ 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2 ],
  [ 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1 ], 
[ 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2 ],
  [ 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1 ], 
[ 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2 ],
  [ 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2 ], 
[ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 ] ];;

hexad_codewords:=[[0, 0, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0],
[0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1],
[0, 2, 2, 0, 1, 0, 0, 1, 1, 0, 0, 1],
[0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1],
[0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1],
[1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 1],
[0, 2, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0],
[0, 2, 1, 0, 1, 0, 0, 0, 2, 1, 2, 0],
[0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 0],
[2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2],
[1, 0, 1, 2, 0, 2, 1, 0, 1, 0, 0, 0],
[1, 0, 0, 0, 1, 1, 0, 2, 0, 1, 2, 0],
[0, 0, 0, 0, 1, 2, 0, 1, 2, 1, 0, 2],
[0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 2],
[1, 0, 0, 2, 2, 0, 1, 1, 0, 0, 2, 0],
[1, 0, 1, 1, 2, 0, 2, 0, 0, 0, 0, 2],
[0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2],
[0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 0, 0],
[0, 1, 1, 2, 2, 0, 1, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2],
[1, 0, 1, 2, 1, 0, 0, 0, 0, 2, 1, 0],
[2, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 1],
[1, 0, 0, 0, 1, 1, 0, 2, 0, 1, 2, 0],
[1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 1, 0],
[0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0],
[2, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 0],
[0, 0, 1, 0, 1, 2, 0, 2, 1, 0, 1, 0],
    [2, 0, 2, 2, 0, 0, 0, 1, 1, 0, 1, 0],
    [2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2],
    [0, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 0],
    [0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 1, 1],
    [0, 0, 0, 1, 2, 1, 2, 1, 0, 1, 0, 0],
    [1, 0, 1, 2, 0, 2, 1, 0, 1, 0, 0, 0],
    [1, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0],
    [2, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0, 0],
    [2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1],
    [1, 1, 0, 2, 0, 0, 0, 0, 1, 1, 2, 0],
    [0, 1, 0, 2, 2, 2, 0, 1, 1, 0, 0, 0],
     [1, 2, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0],
     [0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 1, 0],
     [2, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 1],
     [0, 2, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0],
     [0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 0],
     [0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 2, 1],
     [0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 0, 0],
    [0, 0, 0, 1, 2, 0, 1, 0, 0, 2, 1, 1],
    [1, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 1],
    [0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0],
    [2, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1],
    [0, 2, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2],
    [1, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 1],
    [0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0],
   [2, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2],
    [1, 0, 2, 0, 2, 1, 1, 0, 0, 2, 0, 0],
    [1, 1, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0],
    [0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1],
   [0, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0, 0],
    [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 2, 2],
     [0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 0],
     [1, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0],
     [0, 0, 0, 1, 1, 2, 2, 0, 1, 0, 0, 1],
    [1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0],
    [0, 1, 0, 2, 0, 2, 1, 0, 0, 0, 2, 1],
    [0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2],
     [1, 0, 1, 0, 2, 0, 0, 1, 1, 1, 0, 0],
   [0, 1, 2, 0, 0, 0, 1, 2, 0, 2, 0, 1],
   [0, 2, 0, 1, 2, 0, 0, 0, 1, 1, 0, 2],
  [0, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1, 0],
   [0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1],
   [0, 0, 1, 0, 2, 2, 1, 1, 0, 0, 0, 1],
   [2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1],
   [0, 1, 0, 0, 1, 0, 2, 2, 1, 1, 0, 0],
   [2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0],
   [0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0],
   [0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1],
   [1, 2, 0, 1, 0, 0, 2, 1, 1, 0, 0, 0],
   [1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2],
   [2, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0],
   [1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 0],
    [2, 1, 0, 0, 0, 2, 2, 0, 1, 0, 1, 0],
   [0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1],
   [2, 2, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0],
    [0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2],
   [1, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 1],
   [2, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 0],
  [0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0],
   [1, 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 1],
   [1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0],
   [1, 1, 2, 0, 1, 0, 0, 0, 0, 1, 0, 2],
   [0, 0, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0],
   [0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 2],
   [1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2],
  [2, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 1],
    [0, 1, 0, 2, 1, 0, 0, 0, 2, 2, 0, 1],
    [1, 1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0],
   [2, 1, 1, 0, 0, 0, 0, 2, 0, 1, 1, 0],
   [0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 2, 1],
   [1, 0, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0],
   [1, 0, 2, 0, 0, 2, 0, 0, 2, 1, 1, 0],
   [2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1],
   [0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 0, 0],
   [1, 2, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0],
   [1, 2, 0, 0, 2, 0, 2, 0, 0, 1, 1, 0],
   [1, 1, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0],
   [0, 0, 0, 1, 2, 1, 2, 1, 0, 1, 0, 0],
   [0, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0],
   [1, 1, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0],
   [0, 2, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0],
   [0, 2, 1, 1, 0, 0, 1, 0, 2, 0, 0, 1],
   [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 2, 0],
   [0, 0, 0, 0, 2, 2, 1, 0, 1, 1, 2, 0],
   [0, 2, 1, 0, 2, 1, 2, 0, 1, 0, 0, 0],
   [1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2],
   [0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0],
   [0, 2, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0],
   [0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1],
   [2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0],
   [1, 2, 0, 0, 2, 1, 0, 1, 0, 0, 0, 2],
   [0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1],
   [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 1],
   [2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1],
   [2, 0, 0, 1, 0, 2, 0, 2, 1, 1, 0, 0],
  [0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2],
   [1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0],
   [1, 2, 0, 1, 0, 0, 2, 1, 1, 0, 0, 0],
   [1, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 1],
   [2, 0, 0, 2, 1, 2, 0, 0, 2, 0, 2, 0],
   [2, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2],
  [2, 0, 1, 0, 1, 2, 2, 0, 0, 1, 0, 0],
   [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 2, 2],
   [1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 1],
   [0, 2, 1, 0, 0, 1, 0, 2, 0, 0, 2, 1],
   [1, 0, 0, 0, 0, 2, 0, 1, 1, 0, 2, 1],
   [0, 0, 0, 1, 2, 0, 1, 0, 0, 2, 1, 1],
  [2, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 0],
   [0, 0, 0, 1, 0, 2, 1, 1, 2, 0, 1, 0],
   [2, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0],
  [0, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1],
   [0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 1, 1],
   [1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1],
   [0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 1, 2],
   [1, 2, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0],
   [1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0],
   [0, 1, 2, 0, 2, 0, 0, 0, 1, 2, 1, 0],
   [2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0],
    [1, 1, 0, 2, 0, 0, 0, 0, 1, 1, 2, 0],
   [0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1],
   [0, 1, 1, 2, 0, 1, 0, 0, 2, 0, 1, 0],
   [0, 2, 0, 1, 0, 1, 2, 0, 0, 0, 1, 2],
   [1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 1],
   [0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2],
   [0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2],
   [1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2],
  [0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 0],
   [1, 1, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0],
   [2, 2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 1],
  [2, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 2],
    [1, 1, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0],
   [0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0],
   [1, 0, 1, 2, 1, 0, 0, 0, 0, 2, 1, 0],
   [1, 0, 2, 0, 0, 0, 1, 1, 2, 0, 0, 2],
   [2, 1, 1, 0, 0, 0, 0, 2, 0, 1, 1, 0],
   [2, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1],
   [1, 1, 2, 1, 0, 0, 1, 0, 0, 0, 1, 0],
   [1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2],
   [0, 0, 1, 0, 1, 2, 0, 2, 1, 0, 1, 0],
   [0, 1, 0, 0, 1, 0, 2, 2, 1, 1, 0, 0],
   [0, 0, 2, 1, 2, 0, 1, 2, 1, 0, 0, 0],
   [1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 2],
   [0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2],
   [2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0],
  [2, 2, 2, 0, 0, 0, 1, 0, 1, 1, 0, 0],
   [0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2],
   [0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 1, 2],
    [1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0],
   [0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2],
   [0, 0, 0, 2, 0, 0, 1, 1, 1, 1, 0, 1],
   [0, 1, 2, 1, 2, 1, 0, 0, 0, 0, 0, 1],
   [0, 0, 1, 2, 2, 0, 0, 0, 1, 0, 2, 1],
   [0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0],
   [0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 1, 1],
   [0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2],
    [0, 1, 1, 2, 2, 0, 1, 0, 0, 1, 0, 0],
   [0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2],
   [0, 1, 2, 1, 2, 1, 0, 0, 0, 0, 0, 1],
  [0, 0, 0, 0, 2, 0, 2, 1, 1, 0, 1, 2],
   [2, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1],
   [2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0],
   [0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2],
   [0, 0, 1, 1, 1, 0, 0, 2, 0, 1, 0, 1],
   [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2],
   [0, 0, 1, 0, 2, 2, 1, 1, 0, 0, 0, 1],
   [2, 2, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0],
   [0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 2],
   [0, 0, 1, 2, 1, 0, 2, 1, 2, 0, 0, 0],
   [1, 1, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1],
   [0, 0, 0, 1, 0, 2, 1, 1, 2, 0, 1, 0],
   [2, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1],
   [0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 1, 2],
   [2, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 0],
   [2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0],
   [0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 2, 1],
   [0, 0, 1, 2, 0, 1, 2, 0, 0, 2, 0, 1],
   [2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 2],
   [2, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 2],
   [1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0],
   [1, 2, 0, 1, 1, 0, 0, 0, 0, 0, 2, 1],
   [0, 0, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0],
   [1, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 0],
    [0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 2, 1],
   [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0],
   [2, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0],
   [2, 0, 0, 1, 1, 0, 2, 2, 0, 0, 1, 0],
    [1, 0, 0, 0, 0, 2, 0, 1, 1, 0, 2, 1],
   [1, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 1],
   [1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 2],
   [0, 2, 1, 1, 0, 0, 1, 0, 2, 0, 0, 1],
   [0, 0, 2, 1, 1, 0, 0, 0, 2, 0, 1, 2],
   [0, 1, 0, 2, 0, 0, 2, 1, 0, 2, 1, 0],
   [0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0],
    [2, 0, 2, 2, 1, 0, 1, 0, 0, 0, 0, 1],
   [1, 0, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0],
   [0, 1, 1, 0, 1, 1, 0, 1, 0, 2, 0, 0],
   [1, 1, 2, 0, 1, 0, 0, 0, 0, 1, 0, 2],
   [0, 0, 0, 1, 1, 2, 2, 0, 1, 0, 0, 1],
   [0, 2, 2, 0, 1, 0, 0, 1, 1, 0, 0, 1],
    [1, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 1],
   [0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 2, 1],
   [2, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2],
   [2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1, 2],
   [1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0],
   [0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0],
   [0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1],
   [0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 0],
   [2, 2, 1, 2, 0, 0, 2, 0, 0, 0, 2, 0],
   [1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2],
   [0, 2, 0, 1, 0, 0, 1, 2, 0, 1, 2, 0],
   [1, 0, 0, 2, 0, 1, 0, 1, 2, 2, 0, 0],
   [0, 0, 0, 0, 2, 1, 0, 2, 1, 2, 0, 1],
   [2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0],
   [2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1],
  [0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 1, 0],
   [0, 2, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0],
   [0, 2, 2, 2, 0, 1, 1, 1, 0, 0, 0, 0],
   [2, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2],
  [0, 2, 1, 0, 0, 0, 2, 1, 0, 1, 0, 2],
   [2, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 1],
   [2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0],
   [0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 0, 2],
   [0, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 0],
   [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 2],
   [0, 2, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0],
  [1, 2, 0, 1, 1, 0, 0, 0, 0, 0, 2, 1],
   [1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1],
   [0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 1, 1],
   [1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 0],
   [2, 0, 2, 0, 1, 0, 0, 2, 2, 2, 0, 0],
   [2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 2],
  [0, 1, 1, 2, 0, 1, 0, 0, 2, 0, 1, 0],
   [1, 1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0],
   [2, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2],
   [2, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0, 0],
    [1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2],
    [0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 1, 0]];;;

wt6_codewords:=hexad_codewords;

codewords_min_wt:=function(C)
#returns all code words of minimum
#weight (by a slow brute force search)
#assumes MinimumDistance is correct
local d,i,c,L;
L:=[];
d:=MinimumDistance(C);
for c in C do
 if d=WeightCodeword(c) then Add(L,c); fi;
od;
return L;
end;

codewords_wt:=function(C,k)
#returns all code words of 
#weight k (by a slow brute force search)
local i,c,L;
L:=[];
for c in C do
 if k=WeightCodeword(c) then Add(L,c); fi;
od;
return L;
end;

support_3x4:=function(c)
    # c is a codeword in Golay 12,6,6
    # returns 3x4 block version of c
    local i,j,A,c0;
A:=[];
c0:=VectorCodeword(c);
for i in [1..3] do
 A[i]:=[];
 for j in [1..4] do
         A[i][j]:=c0[(i-1)*4+j]; 
 od;
od;
return A;
end;

support2shuffle:=function(S)
#S is a sublist of [1..12]
local i,L;
L:=[];
for i in S do
if i=1 then Add(L,6); fi;
if i=2 then Add(L,3); fi;
if i=3 then Add(L,0); fi;
if i=4 then Add(L,9); fi;
if i=5 then Add(L,5); fi;
if i=6 then Add(L,2); fi;
if i=7 then Add(L,7); fi;
if i=8 then Add(L,10); fi;
if i=9 then Add(L,4); fi;
if i=10 then Add(L,1); fi;
if i=11 then Add(L,8); fi;
if i=12 then Add(L,11); fi;
od;
return L;
end;


support_word:=function(c)
#c is a list
local i,S;
S:=[];
for i in [1..Length(c)] do
if c[i]<>0 then Add(S,i); fi;
od;
return S;
end;

hexad2support:=function(L)
#L is a hexad in S(5,6,12)
#returns "support" associated to L
local i,L0,x,S,j,c,w;
L0:=[];
for i in L do
 if i=0 then x:=3; fi;
 if i=1 then x:=10; fi;
 if i=2 then x:=6; fi;
 if i=3 then x:=2; fi;
 if i=4 then x:=9; fi;
 if i=5 then x:=5; fi;
 if i=6 then x:=1; fi;
 if i=7 then x:=7; fi;
 if i=8 then x:=11; fi;
 if i=9 then x:=4; fi;
 if i=10 then x:=8; fi;
 if i=11 then x:=12; fi;
 Add(L0,x);
od;
Sort(L0);
return L0;
end;

##"lookup table"
hexad2codeword:=function(L)
#L is a hexad in S(5,6,12)
#returns all wt 6 codewords associated to L
local i,L0,x,S,j,c,w,S1;
#L0:=hexad2support(L);
L0:=L;
Sort(L0);
for x in hexad_codewords do
S:=support_word(x);
S1:=support2shuffle(S);
Sort(S1);
#if S1[1]=L0[1] then Print(S1 in hexads,"  ",S1,"  ",L0,"  \n"); fi;
 if S1=L0 then
   return [x,2*x mod 3];
 fi;
od;
return 0;
end;

best_wt12:=function(r)
#returns the wt 12 codeword c (if any - 0 if not)
#for which r+c has best weight
local x,c,s,s0;
s0:=Length(support_word(r));
s:=Length(support_word(r));
for x in wt12_codewords do
#Print(x,"  ",(r+x) mod 3," \n");
 if Length(support_word((r+x) mod 3))<=6 then
  s:=Length(support_word((r+x) mod 3));
  c:=x;
#Print(s,"  ",s0,"  ",AbsInt(6-Length(support_word((r+x) mod 3))),"  ",AbsInt(6-s0),"  ",x,"  ",support_word((r+x) mod 3)," \n\n");
 fi;
od;
if s<s0 then return c; fi;
return [0,0,0,0,0,0,0,0,0,0,0,0];
end;

find_best_hexad:=function(L)
#L is the support of some word, returns
#hexad best matching L
local i,j,n,h,x,s,L0;
s:=support2shuffle(L);
n:=0;
L0:=[];
for x in hexads do
 if Length(Intersection(s,x))>n then
  n:=Length(Intersection(s,x));
  h:=x;
  Add(L0,x);
#Print(s,"  ",x,"  ",Length(Intersection(s,x))," \n");
 fi;
od;
return h;
end;

find_best_hexads:=function(L)
#L is the support of some word, returns
#hexad best matching L
local i,j,n,h,x,s,L0,L1,m;
s:=support2shuffle(L);
n:=0;
L0:=[];
for x in hexads do
 if Length(Intersection(s,x))>3 then 
  Add(L0,x);
 fi;
od;
m:=Maximum(List(L0,x->Length(x)));
L1:=[];
for x in L0 do
 if Length(x)=m then Add(L1,x); fi;
od;
return L1;
end;

decode2:=function(r)
#does ordinary decoding if e=2 and partial list
#decoding if e>2
local c,cp,cpp,i,H,m,C,rp,rpp,s,h,x,l1,l2;
# decode small wt words
if Length(support_word(r))<=2 then return [0,0,0,0,0,0,0,0,0,0,0,0]; fi;
# decode large wt words
if  Length(support_word(r))>9 then 
 for x in wt12_codewords do
  if Length(support_word((r+x) mod 3))<=2 then 
#    Print("111111\n\n");
    return -x mod 3;
  fi;
 od; 
fi;
rp:=r;
c:=[0,0,0,0,0,0,0,0,0,0,0,0];
for i in [1..100] do
 cp:=Random(wt6_codewords);
 rp:=(rp+cp) mod 3;
 c:=(c-cp) mod 3;
 if Length(support_word(rp))<=2 then return c; fi;
od;
Print("fail\n");
end;
 
decode:=function(r)
#does ordinary decoding if e=2 and partial list
#decoding if e>2
local c,cp,cpp,i,H,m,C,rp,rpp,s,h,x,l1,l2,ell;
ell:=Length(support_word(r));
# decode small wt words
if ell<=2 then return [0,0,0,0,0,0,0,0,0,0,0,0]; fi;
# decode large wt words
if  ell>9 then 
 for x in wt12_codewords do
  if Length(support_word((r+x) mod 3))<=2 then 
    return -x mod 3;
  fi;
 od; 
fi;
if ell>=7 then cp:=best_wt12(r); fi;
if ell<8 then cp:=[0,0,0,0,0,0,0,0,0,0,0,0]; fi;
rp:=(r+cp) mod 3;
if Length(support_word(rp))<=2 then return -cp mod 3; fi;
s:=support_word(rp);
H:=Set(find_best_hexads(s));
C:=[];
for h in H do 
 cpp:=hexad2codeword(h);
 c:=(-cp-cpp[1]) mod 3; Add(C,c); 
 c:=(-cp-cpp[2]) mod 3; Add(C,c); 
od;
m:=Minimum(List(C,c->Length(support_word((r-c) mod 3))));
#Print(C," ------", m,"  \n\n");
for c in C do
 if Length(support_word((r-c) mod 3))=m then return c; fi;
od;
#return C;
end;