#Isaac Lam, HW#13, March 1 2024

#old code
#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:

#MinW(q,M): The minimal weight of the Linear code generated by M over GF(q)
MinW:=proc(q,M) local n,C,c:
n:=nops(M[1]):
C:=LtoC(q,M):

min( seq(HD(c,[0$n]), c in C minus {[0$n]} )):

end:

#start new code for C12.txt: The generator matrix for the cyclic code <g(x)> over R_n (mod x^n-1)
CtoL:=proc(n,x,g) local r,L,i:
r:=degree(g,x):
L:=[seq(coeff(g,x,i),i=0..r)]:
[seq([0$i,op(L), 0$(n-r-1-i)],i=0..n-r-1)]:
end:

with(combinat):
#AllFactors(n,q,x): all the factors of x^n-1 mod q (q is a prime) 
AllFactors:=proc(n,q,x) local S,s:
S:=Factor(x^n-1) mod q:
S:=powerset({op(S)}) minus {{},{op(S)}}:

{seq(expand(convert(s,`*`)) mod q,s in S)}:
end:
#end of old code

CCshopF := proc(N, q, x, K, R, W) local n, C, S, M, g, w; 
C := {}; 
for n from 2 to N do 
 S := AllFactors(n, q, x); 
 for g in S do M := CtoL(n, x, g); 
 if q^nops(M) <= K then 
  w := MinW(q, M); 
  if R <= nops(M)/n and W <= w then 
   C := C union {[g, evalf(nops(M)/n), w]}; 
  end if; 
 end if; 
end do; 
end do; 
C; 
end;

#I have to admit I've been looking for a while and can't see how CtoL with a minor change to account for q isn't already a way to implement 12.15`
CtoDual:=proc(n,q,x,g) local p,r,L,i:
r:=degree(g,x):
P:= g mod q:
L:=[seq(coeff(p,x,i),I=0..r)]:
[seq([0$i,op(L), 0$(n-r-1-i)],i=0..n-r-1)]:
end: