#Isaac Lam, HW5, Feb 7 2024

#Old Class Code

BDfano:=proc():
{{1,2,4},{2,3,5},{3,4,6},{4,5,7},{5,6,1},{6,7,2},{7,1,3}}:
end:

BDex212:=proc():
{{1,3,4,5,9},
{2,4,5,6,10},
{3,5,6,7,11},
{1,4,6,7,8},
{2,5,7,8,9},
{3,6,8,9,10},
{4,7,9,10,11},
{1,5,8,10,11},
{1,2,6,9,11},
{1,2,3,7,10},
{2,3,4,8,11}
}
end:


#SPB(q,n,d): The best you can hope for (as far as the size of C) for q-ary (n,2*t+1) code
SPB:=proc(q,n,t) local i:
trunc(q^n/add(binomial(n,i)*(q-1)^i,i=0..t)):
end:

#SP(q,c,t): the set of all vectors in Fqn(q,n) whose distance is <=t from c
SP:=proc(q,c,t) local S,s,i:
S:={c}:
for i from 1 to t do
 S:=S union {seq(op(Nei(q,s)),s in S)}:
od:
S:
end:

GRC:=proc(q,n,d) local S,A,v:
A:=Fqn(q,n):
S:={}:
while A<>{} do:
 v:=A[1]:
 S:=S union {v}:
 A:=A minus SP(q,v,d-1):
od:
S:
end:

#End of Old Class code

#How I calcullated 3-5

Q2 := Matrix(3, 16, -1);
Q2D := Matrix(3, 16, -1);
for n from 5 to 20 do
    Q2[1, n - 4] := nops(GRC(2, n, 3));
    Q2[2, n - 4] := nops(GRC(2, n, 5));
    Q2[3, n - 4] := nops(GRC(2, n, 7));
    Q2D[1, n - 4] := nops(GRC(2, n, 3)) - SPB(2, n - 4, 3);
    Q2D[2, n - 4] := nops(GRC(2, n, 5)) - SPB(2, n - 4, 5);
    Q2D[3, n - 4] := nops(GRC(2, n, 7)) - SPB(2, n - 4, 7);
end do;
Q3 := Matrix(3, 6, -1);
Q3D := Matrix(3, 6, -1);
for n from 5 to 10 do
    Q3[1, n - 4] := nops(GRC(3, n, 3));
    Q3[2, n - 4] := nops(GRC(3, n, 5));
    Q3[3, n - 4] := nops(GRC(3, n, 7));
    Q3D[1, n - 4] := nops(GRC(3, n, 3)) - SPB(3, n - 4, 3);
    Q3D[2, n - 4] := nops(GRC(3, n, 5)) - SPB(3, n - 4, 5);
    Q3D[3, n - 4] := nops(GRC(3, n, 7)) - SPB(3, n - 4, 7);
end do;
Q5 := Matrix(3, 3, -1);
Q5D := Matrix(3, 3, -1);
for n from 5 to 7 do
    Q5[1, n - 4] := nops(GRC(5, n, 3));
    Q5[2, n - 4] := nops(GRC(5, n, 5));
    Q5[3, n - 4] := nops(GRC(5, n, 7));
    Q5D[1, n - 4] := nops(GRC(5, n, 3)) - SPB(5, n - 4, 3);
    Q5D[2, n - 4] := nops(GRC(5, n, 5)) - SPB(5, n - 4, 5);
    Q5D[3, n - 4] := nops(GRC(5, n, 7)) - SPB(5, n - 4, 7);
end do;


#6. skipped

#7.
PlotkinBound:=proc(n,d):
if n<2*d then
 return 2*trunc(d/(2*d-n)):
end if:
end:

# Code for comparing bounds, plotkin bound is greater
L:=[];
for d from 2 to 20 do
  for n from 2 to 2*d do
    L:=[op(L),[PlotkinBound(n,d),SPB(2,n,d)]]:
  end do:
end do: