#GLORIA LIU, Feb 17 2024, Assignment 8

read `C9.txt`:

#=====================================#
#1. Write a Maple procedure
#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)
#over all the q^d vectors v in the code (including the zero-vector of weight 0)

wt:=proc(v) local i, result:
result:=0:
for i in v do
 if i<>0 then
  result:=result + 1:
 fi:
od:
result:
end:

WtEnumerator:=proc(q,M,t) local C,v:
C:=LtoC(q,M):
add(t^(wt(v)), v in C):
end:

#=====================================#
#2. Find a relation between WtEnumerator(q,M,t) and WtEnumerator(q,H,t) where H is the PCM(q,M) (and 
#hence a generating matrix for the dual code). First do it for q=2, then for other q, and try to 
#discover the relation (if it exists)
result:=Array(1..3, 7..10, 1..2, []):
for i from 1 to 3 do:
 for n from 7 to 10 do:
  k:=rand(1..n-1)():
  q:=ithprime(i):
  M1:=[seq(RV(q,n), i=1..k)]:
  M:=SFde(q,M1):
  H:=PCM(q,M):
  result[i,n,1]:=WtEnumerator(q,M,t):
  print("M",result[i,n,1]);
  result[i,n,2]:=WtEnumerator(q,H,t):
  print("H",result[i,n,2]);
 od:
od:
result;

#I am not sure of the relation between the WtEnumerator of M and H.