Best found linear codes over GR(16,4) of size 4^7:
To get more detailed infos about the codes, click on the entries in the table.
For an explanation of what the different colors mean, look
below
.
n
best
2+1+1+1+1+1
2+2+1+1+1
2+2+2+1
4
4
4
5
6
4
6
6
8
4
8
8
7
12
8
8
12
8
16
8
12
16
9
18
12
16
18
10
22
16
20
22
11
24
20
24
24
12
28
24
24
28
13
31
24
28
31
14
33
28
32
33
15
36
28
32
36
16
40
32
36
40
17
43
36
40
43
18
44
36
40
44
19
48
40
44
48
20
52
44
48
52
21
56
44
52
56
22
56
48
52
56
23
60
52
56
60
24
64
56
60
64
25
66
56
60
66
26
69
60
64
69
27
72
64
68
72
28
76
64
72
76
29
78
68
72
78
30
80
72
76
80
31
84
76
80
84
32
88
76
84
88
33
89
80
84
89
34
92
84
88
92
35
96
84
92
96
36
99
88
92
99
37
101
92
96
101
38
104
96
100
104
39
108
96
104
108
40
112
100
104
112
41
113
104
108
113
42
116
104
112
116
43
120
108
116
120
44
123
112
116
123
45
124
112
120
124
46
128
116
124
128
47
131
120
128
131
48
134
124
128
134
49
137
124
132
137
50
140
128
136
140
51
144
132
139
144
52
146
136
140
146
53
149
136
144
149
54
152
140
148
152
55
156
144
151
156
56
158
144
152
158
57
160
148
156
160
58
164
152
160
164
59
167
156
162
167
60
169
156
164
169
61
173
160
168
173
62
176
164
172
176
63
180
168
175
180
64
182
168
176
182
65
187
172
180
187
66
188
176
184
188
67
192
176
184
192
68
193
180
188
193
69
196
184
192
196
70
200
188
196
200
71
202
188
196
202
72
206
192
200
206
73
208
196
204
208
74
212
200
207
212
75
214
200
208
214
76
217
204
212
217
77
220
208
216
220
78
224
212
220
224
79
226
212
220
226
80
229
216
224
229
81
232
220
228
232
82
236
220
231
236
83
240
224
232
240
84
240
228
236
240
85
244
232
240
244
86
248
232
243
248
87
250
236
244
250
88
253
240
248
253
89
256
244
252
256
90
259
244
254
259
91
262
248
256
262
92
264
252
260
264
93
268
256
264
268
94
271
256
265
271
95
273
260
268
273
96
276
264
272
276
97
280
264
276
280
98
284
268
278
284
99
287
272
280
287
The color scheme indicates how the homogeneous minimum distance of the entry compares to that of other linear codes over GR(16,4) of the same length and size 4^7.
It is as follows:
d
This code has the best minimum distance within our database, however it is possible that better ones exist.
d
This code has optimal minimum distance.
d
There are better codes of same size and length but different shape in the database.
Best found linear codes over GR(16,4) in dependence of the size
Comparison of the Gray images for q = 4 and size = 4^7