Information on Result #617809

Linear OA(2774, 729, F27, 39) (dual of [729, 655, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2793, 757, F27, 39) (dual of [757, 664, 40]-code) [i](u, u+v)-Construction
2Linear OA(2794, 767, F27, 39) (dual of [767, 673, 40]-code) [i]
3Linear OA(2795, 777, F27, 39) (dual of [777, 682, 40]-code) [i]
4Linear OA(2796, 781, F27, 39) (dual of [781, 685, 40]-code) [i]
5Linear OA(2797, 793, F27, 39) (dual of [793, 696, 40]-code) [i]
6Linear OA(2798, 797, F27, 39) (dual of [797, 699, 40]-code) [i]
7Linear OA(2799, 805, F27, 39) (dual of [805, 706, 40]-code) [i]
8Linear OA(27100, 811, F27, 39) (dual of [811, 711, 40]-code) [i]
9Linear OA(27101, 813, F27, 39) (dual of [813, 712, 40]-code) [i]
10Linear OA(27102, 817, F27, 39) (dual of [817, 715, 40]-code) [i]
11Linear OA(27103, 823, F27, 39) (dual of [823, 720, 40]-code) [i]
12Linear OA(27104, 825, F27, 39) (dual of [825, 721, 40]-code) [i]
13Linear OA(27105, 827, F27, 39) (dual of [827, 722, 40]-code) [i]
14Linear OA(27106, 829, F27, 39) (dual of [829, 723, 40]-code) [i]
15Linear OA(27107, 834, F27, 39) (dual of [834, 727, 40]-code) [i]
16Linear OA(27109, 912, F27, 39) (dual of [912, 803, 40]-code) [i]
17Linear OA(27110, 1094, F27, 39) (dual of [1094, 984, 40]-code) [i]
18Linear OA(27108, 841, F27, 39) (dual of [841, 733, 40]-code) [i]
19Linear OA(27109, 765, F27, 39) (dual of [765, 656, 40]-code) [i]Generalized (u, u+v)-Construction
20Linear OA(27108, 764, F27, 39) (dual of [764, 656, 40]-code) [i]
21Linear OA(27105, 761, F27, 39) (dual of [761, 656, 40]-code) [i]
22Linear OA(27108, 765, F27, 39) (dual of [765, 657, 40]-code) [i]
23Linear OA(27110, 769, F27, 39) (dual of [769, 659, 40]-code) [i]
24Linear OA(27103, 759, F27, 39) (dual of [759, 656, 40]-code) [i]
25Linear OA(27105, 762, F27, 39) (dual of [762, 657, 40]-code) [i]
26Linear OA(27107, 765, F27, 39) (dual of [765, 658, 40]-code) [i]
27Linear OA(27109, 768, F27, 39) (dual of [768, 659, 40]-code) [i]
28Linear OA(27110, 771, F27, 39) (dual of [771, 661, 40]-code) [i]
29Linear OA(27101, 757, F27, 39) (dual of [757, 656, 40]-code) [i](u, u−v, u+v+w)-Construction
30Linear OA(27102, 759, F27, 39) (dual of [759, 657, 40]-code) [i]
31Linear OA(27103, 761, F27, 39) (dual of [761, 658, 40]-code) [i]
32Linear OA(27104, 763, F27, 39) (dual of [763, 659, 40]-code) [i]
33Linear OA(27105, 765, F27, 39) (dual of [765, 660, 40]-code) [i]
34Linear OA(27106, 785, F27, 39) (dual of [785, 679, 40]-code) [i]
35Linear OA(27107, 795, F27, 39) (dual of [795, 688, 40]-code) [i]
36Linear OA(27108, 805, F27, 39) (dual of [805, 697, 40]-code) [i]
37Linear OA(27109, 815, F27, 39) (dual of [815, 706, 40]-code) [i]
38Linear OA(27110, 825, F27, 39) (dual of [825, 715, 40]-code) [i]
39Linear OA(2776, 731, F27, 40) (dual of [731, 655, 41]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
40Linear OA(2774, 731, F27, 39) (dual of [731, 657, 40]-code) [i]✔
41Linear OA(2779, 734, F27, 41) (dual of [734, 655, 42]-code) [i]✔
42Linear OA(2775, 734, F27, 39) (dual of [734, 659, 40]-code) [i]✔
43Linear OA(2782, 737, F27, 42) (dual of [737, 655, 43]-code) [i]✔
44Linear OA(2776, 737, F27, 39) (dual of [737, 661, 40]-code) [i]✔
45Linear OA(2785, 740, F27, 43) (dual of [740, 655, 44]-code) [i]✔
46Linear OA(2777, 740, F27, 39) (dual of [740, 663, 40]-code) [i]✔
47Linear OA(2788, 743, F27, 44) (dual of [743, 655, 45]-code) [i]✔
48Linear OA(2778, 743, F27, 39) (dual of [743, 665, 40]-code) [i]✔
49Linear OA(2791, 746, F27, 45) (dual of [746, 655, 46]-code) [i]✔
50Linear OA(2779, 746, F27, 39) (dual of [746, 667, 40]-code) [i]✔
51Linear OA(2794, 749, F27, 46) (dual of [749, 655, 47]-code) [i]✔
52Linear OA(2780, 749, F27, 39) (dual of [749, 669, 40]-code) [i]✔
53Linear OA(2797, 752, F27, 47) (dual of [752, 655, 48]-code) [i]✔
54Linear OA(2781, 752, F27, 39) (dual of [752, 671, 40]-code) [i]✔
55Linear OA(27100, 755, F27, 48) (dual of [755, 655, 49]-code) [i]✔
56Linear OA(2782, 755, F27, 39) (dual of [755, 673, 40]-code) [i]✔
57Linear OA(27103, 757, F27, 49) (dual of [757, 654, 50]-code) [i]✔
58Linear OA(27104, 759, F27, 49) (dual of [759, 655, 50]-code) [i]✔
59Linear OA(2783, 757, F27, 39) (dual of [757, 674, 40]-code) [i]✔
60Linear OA(2784, 759, F27, 39) (dual of [759, 675, 40]-code) [i]✔
61Linear OA(27107, 762, F27, 50) (dual of [762, 655, 51]-code) [i]✔
62Linear OA(2785, 761, F27, 39) (dual of [761, 676, 40]-code) [i]✔
63Linear OA(27110, 765, F27, 51) (dual of [765, 655, 52]-code) [i]✔
64Linear OA(2787, 765, F27, 39) (dual of [765, 678, 40]-code) [i]✔
65Linear OA(2788, 767, F27, 39) (dual of [767, 679, 40]-code) [i]✔
66Linear OA(2789, 769, F27, 39) (dual of [769, 680, 40]-code) [i]✔
67Linear OA(2790, 772, F27, 39) (dual of [772, 682, 40]-code) [i]✔
68Linear OA(2791, 775, F27, 39) (dual of [775, 684, 40]-code) [i]✔
69Linear OA(2792, 777, F27, 39) (dual of [777, 685, 40]-code) [i]✔
70Linear OA(2793, 779, F27, 39) (dual of [779, 686, 40]-code) [i]✔
71Linear OA(2794, 781, F27, 39) (dual of [781, 687, 40]-code) [i]✔
72Linear OA(2795, 783, F27, 39) (dual of [783, 688, 40]-code) [i]✔
73Linear OA(2796, 786, F27, 39) (dual of [786, 690, 40]-code) [i]✔