#George Spahn
#2/25/2024
#OK TO POST

#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:

#TRA(M): inputs a matrix M as a list of lists outputs the transpose matrix
#also as a list of lists
TRA:=proc(M) local i,j:[seq([seq(M[j][i],j=1..nops(M))],i=1..nops(M[1]))]:end:



isg := proc(v)
local i:
for i in v do
if i = 1 then 
return(true):
fi:
if i > 1 then 
return(false):
fi:
od:
end:

Hampcm := proc(r,q)
local M,N,i:
M:=Fqn(q,r) minus {[0$r], seq([0$(i-1),1,0$(r-i)],i=1..r)}:
N:=[]:
for i in M do
if isg(i) then
N:=[op(N),i]:
fi:
od:
TRA([op(N),seq([0$(i-1),1,0$(r-i)],i=1..r)]):
end:


Ham := proc(r,q)
antiPCM(q,Hampcm(r,q)):
end:






#start code by Pablo Blanco
# input q, the modulus and a parity check matrix H in standard form. H:= [-A^T | I_{n-k}] has k rows and n columns. 
# outputs M, the corresponding generating matrix. M := [ I_k | A] has n-k rows and n columns. A has k rows and n-k columns.
antiPCM:=proc(q,H) local A,B,M,n,rows,k,co,tempCol:
 rows:=nops(H): # this is n-k
 n:=nops(H[1]): # number of H columns
 k:= n-rows: 

 B:=extractMCols(1,k,H):                         # this is -A^T, we wish to return [I_k | A].
 tempCol := extractMCols(1,1,B):                 # take the first column, negate it
 A:= [[seq(op(tempCol[k]), k=1..nops(tempCol))]]:  # make the first column into a row
 
 for co from 2 to k do:
   tempCol := extractMCols(co,co,B): # take the (co)-th column 
   A:= [op(A), [seq(op(tempCol[k]), k=1..nops(tempCol))]]: # add the co-th column as a row
 od:

 A:= -A mod q: # we took the transpose, now we negate.

 co:=1:
 M:=A:
 for co from 1 to k do: #we will append the identity matrix row by row
  M[co] := [0$(co-1), 1, 0$(k-co),op(A[co])]:
 od:

 M:
end:

# a few helper functions:

# extracts rows i through j of matrix M, returns a matrix with those rows
extractMRows := proc(i,j,M) local colN,k:
 colN:=nops(M[1]): # number of columns of M
 [seq(M[k][1..colN] ,k=i..j)]
end:

# extracts columns i through j of matrix M, returns a matrix with those columns
extractMCols := proc(i,j,M) local rowN,k:
 rowN:= nops(M): # number of rows of M
 [seq( M[k][i..j] , k=1..rowN)]:
end:

# DecodeLT(q,M).
DecodeLT := proc(q,M) local T,n,V,S,v,syn,H:
 option remember:
 n:=nops(M[1]):
 T:= SynT(q,M)[1]:
 V:= Fqn(q,n):
 S:=table():
 H:=PCM(q,M):
 for v in V do:
  syn:= Syn(q,H,v):
  S[v]:= v-T[syn] mod q:
 od:
 op(S):
end:

#End code by Pablo Blanco