Best found linear codes over GR(16,4) of size 4^8:
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+2+1+1+1+1
2+2+2+1+1
2+2+2+2
4
3
3
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
21
16
19
21
11
24
20
22
24
12
25
24
24
25
13
28
24
28
28
14
32
28
28
32
15
35
28
32
35
16
38
32
36
38
17
40
36
39
40
18
44
36
40
44
19
48
40
44
48
20
50
44
48
50
21
52
44
51
52
22
54
48
52
54
23
57
52
56
57
24
60
56
60
60
25
64
56
60
64
26
67
60
64
67
27
70
64
68
70
28
73
71
73
29
76
72
76
30
80
76
80
31
82
80
82
32
86
82
86
33
88
84
88
34
92
88
92
35
92
91
92
36
96
92
96
37
99
96
99
38
102
100
102
39
105
102
105
40
108
104
108
41
111
108
111
42
114
112
114
43
117
114
117
44
120
116
120
45
122
120
122
46
124
123
124
47
128
125
128
48
131
128
131
49
136
132
136
50
137
134
137
51
140
136
140
52
144
140
144
53
145
144
145
54
148
146
148
55
152
148
152
56
156
152
156
57
159
155
159
58
160
157
160
59
163
160
163
60
168
164
168
61
169
167
169
62
172
169
172
63
177
172
177
64
180
176
180
65
181
179
181
66
184
180
184
67
188
184
188
68
192
187
192
69
192
190
192
70
196
192
196
71
199
196
199
72
202
199
202
73
204
202
204
74
208
204
208
75
210
208
210
76
213
211
213
77
216
213
216
78
220
216
220
79
223
220
223
80
225
222
225
81
228
225
228
82
232
228
232
83
234
231
234
84
238
234
238
85
240
236
240
86
244
240
244
87
246
243
246
88
249
245
249
89
252
248
252
90
256
252
256
91
258
255
258
92
261
258
261
93
264
260
264
94
267
264
267
95
269
267
269
96
273
269
273
97
275
272
275
98
280
276
280
99
281
278
281
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 4^8.
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 = 4^8