#HW8 Nuray Kutlu

#Old code from class

#MinD(C): The minimal (Hamming) distance of the code C
MinD:=proc(C) local i,j:
min( seq(seq(HD(C[i],C[j]),j=i+1..nops(C)), i=1..nops(C))):
end:

#HD(u,v): The Hamming distance between two words (of the same length)
HD:=proc(u,v) local i,co:
co:=0:
for i from 1 to nops(u) do
  if u[i]<>v[i] then
      co:=co+1:
  fi:
od:
co:
end:

#LtoC(q,M): inputs a list of basis vectors for our linear code over GF(q)
#outputs all the codewords (the actual subset of GF(q)^n with q^k elements
LtoC:=proc(q,M) local n,k,C,c,i,M1:
option remember:
k:=nops(M):
n:=nops(M[1]):
if k=1 then
 RETURN({seq(i*M[1] mod q,i=0..q-1) }):
fi:
M1:=M[1..k-1]:
C:=LtoC(q,M1):
{seq(seq(c+i*M[k] mod q,i=0..q-1),c in C)}:
end:

#End of old code from class

#WtEnumerator(q,M,t)
#that inputs a generating matrix M (with k rows say, so so it is an [n,k,d] code for some d )
#for a linear code over GF(q) (q prime) and outputs the Sum(t^wt(v), v in C)
#So basically it sums all 
WtEnumerator:=proc(q,M,t) local v, n, k, d, sum, C,w:
sum:=0:
k:=nops(M):
n:=nops(M[1]):
d:= MinD(M):
C:= LtoC(q,M):
for v in C do:
 w := HD(c,[0$n]):
 sum:= sum + t^w:
od:
sum:
end: