#3: Use GRC(q,n,d) with q=2, d=3,5,7, and 5 ≤ n ≤20, for each case find the cardinality of the code (what's called M in the book). Also find the Sphere-Packing Bound. How far are they in each case?
* i accidentally put a -1 in the print statements, please ignore*

temp := GRC(2, 5, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1; -1; 1;');
SPB(2, 5, 1);
temp := GRC(2, 6, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1; -1; 1;');
SPB(2, 6, 1);
temp := GRC(2, 7, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1; -1; 1;');
SPB(2, 7, 1);
temp := GRC(2, 8, 3);
print('calculated; 1;');
nops(temp);
print('best; 1;');
SPB(2, 8, 1);
temp := GRC(2, 9, 3);
print('calculated');
nops(temp);
print('best');
SPB(2, 9, 1);
temp := GRC(2, 10, 3);
print('calculated');
nops(temp);
print('best');
SPB(2, 10, 1);
temp := GRC(2, 11, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 11, 1);
temp := GRC(2, 12, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 12, 1);
temp := GRC(2, 13, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 13, 1);
temp := GRC(2, 14, 3);
print('calculated');
nops(temp);
print('best; 1;');
SPB(2, 14, 1);
temp := GRC(2, 15, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 15, 1);
temp := GRC(2, 16, 3);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 16, 1);
                     calculated; 1; -1; 1;

                               4

                        best; 1; -1; 1;

                               5

                     calculated; 1; -1; 1;

                               8

                        best; 1; -1; 1;

                               9

                     calculated; 1; -1; 1;

                               16

                        best; 1; -1; 1;

                               16

                         calculated; 1;

                               16

                            best; 1;

                               28

                           calculated

                               32

                              best

                               51

                           calculated

                               64

                              best

                               93

                     calculated; 1; -1; 1;

                              128

                            best; 1;

                              170

                     calculated; 1; -1; 1;

                              256

                            best; 1;

                              315

                     calculated; 1; -1; 1;

                              512

                            best; 1;

                              585

                           calculated

                              1024

                            best; 1;

                              1092

                     calculated; 1; -1; 1;

                              2048

                            best; 1;

                              2048

                     calculated; 1; -1; 1;

                              2048

                            best; 1;

                              3855



temp := GRC(2, 5, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 5, 2);
                        calculated; -1;

                               2

                           best; -1;

                               2
temp := GRC(2, 6, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 6, 2);
                        calculated; -1;

                               2

                           best; -1;

                               2

temp := GRC(2, 7, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 7, 2);
                        calculated; -1;

                               2

                           best; -1;

                               4

temp := GRC(2, 8, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 8, 2);
                        calculated; -1;

                               4

                           best; -1;

                               6

temp := GRC(2, 9, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 9, 2);
                        calculated; -1;

                               4

                           best; -1;

                               11

temp := GRC(2, 10, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 10, 2);
                        calculated; -1;

                               8

                           best; -1;

                               18

temp := GRC(2, 11, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 11, 2);
                        calculated; -1;

                               16

                           best; -1;

                               30

temp := GRC(2, 12, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 12, 2);
                        calculated; -1;

                               16

                           best; -1;

                               51

temp := GRC(2, 13, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 13, 2);
                        calculated; -1;

                               32

                           best; -1;

                               89

temp := GRC(2, 14, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 14, 2);
                        calculated; -1;

                               64

                           best; -1;

                              154

temp := GRC(2, 15, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 15, 2);
                        calculated; -1;

                              128

                           best; -1;

                              270

temp := GRC(2, 16, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 16, 2);
                        calculated; -1;

                              256

                           best; -1;

                              478

temp := GRC(2, 17, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 17, 2);
                        calculated; -1;

                              512

                           best; -1;

                              851

temp := GRC(2, 18, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 18, 2);
                        calculated; -1;

                              512

                           best; -1;

                              1524

temp := GRC(2, 19, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 19, 2);
                        calculated; -1;

                              1024

                           best; -1;

                              2744

temp := GRC(2, 20, 5);
print('calculated; -1;');
nops(temp);
print('best; -1;');
SPB(2, 20, 2);
                        calculated; -1;

                              2048

                           best; -1;

                              4969


temp := GRC(2, 5, 7);
print('calculated');
nops(temp);
print('best; 1; -1; 1;');
SPB(2, 5, 3);
temp := GRC(2, 6, 7);
print('calculated; 1;');
nops(temp);
print('best; 1; -1; 1;');
SPB(2, 6, 3);
temp := GRC(2, 7, 7);
print('calculated; 1;');
nops(temp);
print('best; 1; -1; 1;');
SPB(2, 7, 3);
temp := GRC(2, 8, 7);
print('calculated; 1;');
nops(temp);
print('best; 1;');
SPB(2, 8, 3);
temp := GRC(2, 9, 7);
print('calculated');
nops(temp);
print('best');
SPB(2, 9, 3);
temp := GRC(2, 10, 7);
print('calculated');
nops(temp);
print('best');
SPB(2, 10, 3);
temp := GRC(2, 11, 7);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 11, 3);
temp := GRC(2, 12, 7);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 12, 3);
temp := GRC(2, 13, 7);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 13, 3);
temp := GRC(2, 14, 7);
print('calculated');
nops(temp);
print('best; 1;');
SPB(2, 14, 3);
temp := GRC(2, 15, 7);
print('calculated; 1; -1; 1;');
nops(temp);
print('best; 1;');
SPB(2, 15, 3);
temp := GRC(2, 16, 7);
print('calculated; 1;');
nops(temp);
print('best; 1;');
SPB(2, 16, 3);
                           calculated

                               1

                        best; 1; -1; 1;

                               1

                         calculated; 1;

                               1

                        best; 1; -1; 1;

                               1

                         calculated; 1;

                               2

                        best; 1; -1; 1;

                               2

                         calculated; 1;

                               2

                            best; 1;

                               2

                           calculated

                               2

                              best

                               3

                           calculated

                               2

                              best

                               5

                     calculated; 1; -1; 1;

                               4

                            best; 1;

                               8

                     calculated; 1; -1; 1;

                               4

                            best; 1;

                               13

                     calculated; 1; -1; 1;

                               8

                            best; 1;

                               21

                           calculated

                               16

                            best; 1;

                               34

                     calculated; 1; -1; 1;

                               32

                            best; 1;

                               56

                         calculated; 1;

                               32

                            best; 
				94


#4: Use GRC(q,n,d) with q=3, d=3,5,7, and 5 ≤ n ≤10, for each case find the cardinality of the code (what's called M in the book). Also find the Sphere-Packing Bound. How far are they in each case?
GRCval := GRC(3, 5, 3);
M := nops(GRCval);
SPB(3, 5, 1);
GRCval := GRC(3, 6, 3);
M := nops(GRCval);
SPB(3, 6, 1);
GRCval := GRC(3, 7, 3);
M := nops(GRCval);
SPB(3, 7, 1);
GRCval := GRC(3, 8, 3);
M := nops(GRCval);
SPB(3, 8, 1);
GRCval := GRC(3, 9, 3);
M := nops(GRCval);
SPB(3, 9, 1);
GRCval := GRC(3, 10, 3);
M := nops(GRCval);
SPB(3, 10, 1);
                             M := 9
                               22
                            M := 24
                               56
                            M := 72
                              145
                            M := 198
                              385
                            M := 519
                              1035
                           M := 1390
                              2811

GRCval := GRC(3, 5, 5);
M := nops(GRCval);
SPB(3, 5, 2);
GRCval := GRC(3, 6, 5);
M := nops(GRCval);
SPB(3, 6, 2);
GRCval := GRC(3, 7, 5);
M := nops(GRCval);
SPB(3, 7, 2);
GRCval := GRC(3, 8, 5);
M := nops(GRCval);
SPB(3, 8, 2);
GRCval := GRC(3, 9, 5);
M := nops(GRCval);
SPB(3, 9, 2);
GRCval := GRC(3, 10, 5);
M := nops(GRCval);
SPB(3, 10, 2);
                             M := 3
                               4
                             M := 3
                               9
                             M := 8
                               22
                            M := 18
                               50
                            M := 39
                              120
                            M := 83
                              293

GRCval := GRC(3, 5, 7);
M := nops(GRCval);
SPB(3, 5, 3);
GRCval := GRC(3, 6, 7);
M := nops(GRCval);
SPB(3, 6, 3);
GRCval := GRC(3, 7, 7);
M := nops(GRCval);
SPB(3, 7, 3);
GRCval := GRC(3, 8, 7);
M := nops(GRCval);
SPB(3, 8, 3);
GRCval := GRC(3, 9, 7);
M := nops(GRCval);
SPB(3, 9, 3);
GRCval := GRC(3, 10, 7);
M := nops(GRCval);
SPB(3, 10, 3);
                             M := 1
                               1
                             M := 1
                               3
                             M := 3
                               5
                             M := 3
                               11
                             M := 3
                               23
                             M := 9
                               50

#5: USe GRC(q,n,d) with q=5, d=3,5,7, and 5 ≤ n ≤7, for each case find the cardinality of the code (what's called M in the book). Also find the Sphere-Packing Bound. How far are they in each case?
GRCval := GRC(5, 5, 3):
M := nops(GRCval);
SPB(5, 5, 1);
GRCval := GRC(5,6, 3):
M := nops(GRCval);
SPB(5, 6, 1);
GRCval := GRC(5, 7, 3):
M := nops(GRCval);
SPB(5, 7, 1);
print('next set'):
GRCval := GRC(5, 5, 5):
M := nops(GRCval);
SPB(5, 5, 2);
GRCval := GRC(5,6, 5):
M := nops(GRCval);
SPB(5, 6, 2);
GRCval := GRC(5, 7, 5):
M := nops(GRCval);
SPB(5, 7, 2);
print('next set'):
GRCval := GRC(5, 5, 7):
M := nops(GRCval);
SPB(5, 5, 3);
GRCval := GRC(5,6, 7):
M := nops(GRCval);
SPB(5, 6, 3);
GRCval := GRC(5, 7, 7):
M := nops(GRCval);
SPB(5, 7, 3);

                            M := 74
                              148
                            M := 265
                              625
                           M := 1113
                              2693
                          *(next, set)
                             M := 5
                               17
                            M := 13
                               58
                            M := 39
                              214
                          *(next, set)
                             M := 1
                               3
                             M := 1
                               10
                             M := 5
                              29

#7:

PlotkinBound:=proc(n,d) local m:
if d mod 2 = 0 then 
 if 2 * d >n then
  m:= 2*floor(d/(2*d - n)):
 else
  m:=4*d:
 fi:
else
 if 2*d+1 >n then
  m:= 2*floor((d+1)/(2*d+1-n)):
 else
  m:= 4*d+4:
 fi:
fi:
m:
end: