#HW 9 Nuray Kutlu
#OK to post

#Valentine Ages:
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#RDB: ...
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#Shaurya Baranwal: 19


#inputs the modolus q, and a parity check matrix in standard form, outputs the corresponding
# generating matrix M of a linear code over GF(q) such that
#antiPCM(q,PCM(q,M))=M and PCM(q,AntiPCM(q,H))=H
antiPCM:=proc(q,H) local nmk, n,k,i,j,M:
nmk:= nops(H):
n:=nops(H[1]):
k:=n-nmk:
for i from 1 to k do
 for j from 1 to k do
  if j=i then
   M[i,j] := 1:
  else
   M[i,j]:=0:
  fi:
 od:
 for j from k+1 to n do
  M[i,j] = -H[j-k][i] mod q:
 od:
od:

[seq([seq(M[i,j],j=1..n)],i=1..k)]:

end:


#DecodeLT(q,M) :
#that is similar to DecodeT(q,n,C), that inputs a generating matrix M 
#(note that n=nops(M[1])), and uses the Syndrom Table to construct a table that mays 
#every vector in Fqn(q,n) to the member of LtoC(q,M) that it is mapped to.
DecodeLT:=proc(q,M) local n,k,CT,T, C,FQN,v,w, syn, H,cos:
H:= PCM(q, M):
C:=LtoC(q,M):
n:= nops(M[1]):
CT:=SynT(q,M):
FQN:=Fqn(q,n):
for v in FQN do:
 syn:= Syn(q,H,v):
 cos:= SynT[syn]:
 w := v-cos:
 T[v]:=w:
od:
T:
end:

#Old Code from class
#PCM(q,M): inputs the mod. q and a non-empty basis (a list of lists)
#n=nops(M[1]) M is k by n matrix and H=PCM(q,M) is an n-k by n matrix
#describing the basis of some linear code over GF(q)^n outputs of dimension k=nops(M)
#the (n-k) by n
PCM:=proc(q,M) local k,n,i,j,H:
option remember:
k:=nops(M):
n:=nops(M[1]):


SAah:=proc(q,n,M) local SL,C,A,a,r1,r,j:
# copied from class
 C:=LtoC(q,M):
 C:=C minus {[0$n]}:
# added
 r1 := [[0$n],op(C)]:
 SL := [r1]:
 A:=Fqn(q,n) minus {op(r1)}: # changed from class
 while A<>{} do
    # find coset representative of min weight
    a := minW(A) :
    # build next row
    r := []:
    for j from 1 to nops(r1) do
        r := [op(r), a + r1[j] mod q]:
    od:
    # add new row to array
    SL := [op(SL), r];
    
    # print(SL);
    # update available vectors
    A := A minus {op(SL[-1])}:
 od:
SL;
end:

if [seq([op(1..k,M[i])],i=1..k)]<>[seq([0$(i-1),1,0$(k-i)],i=1..k)] then
 print(`Not standard form , please use SFde(q,M) first `):
 RETURN(FAIL):
fi:
for i from 1 to n-k do
 for j from 1 to k do
  H[i,j]:=-M[j][i+k]  mod q:
 od:
 for j from k+1 to n do
  if j-k=i then
   H[i,j]:=1:
  else
   H[i,j]:=0:
  fi:
od:
od:
[seq([seq(H[i,j],j=1..n)],i=1..n-k)]:
end:

#Syn(q,H,y): The syndrom of the transmitted vector y if the PCM is H
#(a row vector of length n-k) 
Syn:=proc(q,H,y) local i:
[seq(DP(q,y,H[i]),i=1..nops(H))]:
end:

#Alphabet {0,1,...q-1}, Fqn(q,n): {0,1,...,q-1}^n
Fqn:=proc(q,n) local S,a,v:
option remember:
if n=0 then
 RETURN({[]}):
fi:
S:=Fqn(q,n-1):
{seq(seq([op(v),a],a=0..q-1), v in S)}:

end: