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State-bounded G-Codes

The following tables contain the code parameters for trellis state-bounded G-codes with log-state bounds of 4 (i.e. 24 = 16 states maximum), 5 (i.e. 25 = 32 states maximum), and 6 (i.e. 26 = 64 states maximum) respectively. For each of these bounds, we list the length of the generated code for each of the minimum distances 4 through 8. Blank entries correspond to codes we have not computed due to limited computational resources. The distance 6 codes have also been plotted in Figure A.7.

Dimension d=4 d=5 d=6 d=7 d=8
1 4 5 6 7 8
2 6 8 9 11 12
3 7 10 11 13 14
4 8 11 12 14 15
5 10 13 14 15 16
6 11 14 15 18 20
7 12 16 17 22 24
8 13 18 19 24 26
9 14 20 21 25 27
10 15 21 23 26 28
11 16 23 25 29 32
12 18 24 27 33 36
13 19 26 29 35
14 20 28 31
15 21 30 33
16 22 31 35
17 23 33 37
18 24 34 39
19 26 36
20 27 38
21 28 40
22 29 41
23 30 43
24 31
25 32
26 34
27 35
28 36
29 37
30 38
31 39
32 40
33 42
34 40
35 41
36 43
37 44
38 45
39 47
40 48
41 49
42 50
43 51
44 52
45 53
46 55
47 56
48 57
49 58
Dimension d=4 d=5 d=6 d=7 d=8
1 4 5 6 7 8
2 6 8 9 11 12
3 7 10 11 13 14
4 8 11 12 14 15
5 10 13 14 14 16
6 11 14 15 17 18
7 12 15 16 19 20
8 13 17 18 22 24
9 14 18 19 24 26
10 15 20 21 25 27
11 16 21 23 27 28
12 18 23 24 29 30
13 19 24 26 31 32
14 20 25 27 33 36
15 21 27 28 35
16 22 28 30 36
17 23 30 31
18 24 31 33
19 25 33 35
20 26 34 36
21 27 35 38
22 28 37 39
23 29 38 40
24 30 40 42
25 31 41 43
26 32 43
27 34 44
28 35 46
29 36 47
30 37 48
31 38 50
32 39 51
33 40 53
34 41 54
35 42 56
36 43 57
37 44 58
38 45
39 46
40 47
41 48
42 50
43 51
44 52
45 53
46 54
47 55
48 56
49 57
Dimension d=4 d=5 d=6 d=7 d=8
1 4 5 6 7 8
2 6 8 9 11 12
3 7 10 11 13 14
4 8 11 12 14 15
5 10 13 14 15 16
6 11 14 15 17 18
7 12 15 16 18 19
8 13 16 17 19 20
9 14 17 18 22 24
10 15 19 20 24 26
11 16 20 21 25 27
12 18 22 23 27 28
13 19 23 25 29 30
14 20 24 26 30 31
15 21 26 27 32 32
16 22 27 29 33 36
17 23 28 30 35 38
18 24 29 31 37 39
19 25 31 33 39 40
20 26 32 34 40 42
21 27 33 36 42 43
22 28 35 37
23 29 36 39
24 30 37 40
25 31 38 41
26 32 40 43
27 34 41 44
28 35 42 45
29 36 44 47
30 37 45 48
31 38 46 50
32 39 48 51
33 40 49 53
34 41 50 54
35 42 51
36 43 53
37 44 54
38 45 55
39 46 57
40 47 58
41 48 59
42 49 61
43 50 62
44 51 63
45 52 64
46 53
47 54
48 55
49 56

Figure: The effects of bounding the state complexity of distance 6 G-codes with various constants.
\resizebox{\linewidth}{!}{\includegraphics{Figures/statebound.eps}}

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Next: Bounding decoding complexity Up: Generalized Lexicodes Previous: Trellis-oriented G-codes   Contents
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