Best found linear codes over GR(16,4) of size 4^6:
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
2+2+1+1
2+2+2
3
3
3
4
6
4
6
5
9
4
8
9
6
12
8
8
12
7
16
8
12
16
8
18
12
16
18
9
22
16
20
22
10
24
20
24
24
11
27
24
24
27
12
31
24
28
31
13
34
28
32
34
14
36
32
34
36
15
40
32
36
40
16
44
36
40
44
17
47
40
43
47
18
49
40
46
49
19
52
44
48
52
20
56
48
52
56
21
60
52
56
60
22
60
56
56
60
23
63
56
60
63
24
66
60
64
66
25
69
64
68
69
26
72
64
70
72
27
75
68
72
75
28
78
72
76
78
29
81
76
80
81
30
83
80
81
83
31
86
80
84
86
32
89
84
88
89
33
92
88
92
92
34
96
88
93
96
35
99
92
96
99
36
102
96
100
102
37
105
96
104
105
38
108
100
104
108
39
112
104
108
112
40
114
108
112
114
41
117
112
116
117
42
120
112
117
120
43
123
116
120
123
44
126
120
124
126
45
128
120
128
128
46
131
124
129
131
47
134
128
132
134
48
137
128
136
137
49
140
132
138
140
50
144
136
141
144
51
147
140
144
147
52
150
144
148
150
53
153
144
152
153
54
156
148
153
156
55
160
152
156
160
56
162
152
160
162
57
165
156
164
165
58
168
160
166
168
59
171
164
168
171
60
176
164
172
176
61
179
168
176
179
62
180
172
178
180
63
184
176
181
184
64
188
176
184
188
65
192
180
188
192
66
192
184
191
192
67
195
188
193
195
68
198
192
196
198
69
200
192
200
200
70
204
196
204
203
71
208
200
205
208
72
210
200
208
210
73
213
204
211
213
74
216
208
216
214
75
220
212
217
220
76
224
212
220
224
77
226
216
224
226
78
229
220
227
229
79
232
224
229
232
80
236
224
233
236
81
237
228
236
237
82
240
232
239
240
83
244
232
241
244
84
248
236
244
248
85
249
240
249
248
86
252
244
251
252
87
256
244
254
256
88
257
248
256
257
89
260
252
260
259
90
264
256
263
264
91
266
256
266
265
92
270
260
270
268
93
272
264
272
272
94
275
268
274
275
95
278
268
278
278
96
281
272
281
280
97
284
276
284
284
98
288
280
288
287
99
291
280
288
291
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 4^6.
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 = 4^6