Information on Result #617539

Linear OA(2735, 729, F27, 18) (dual of [729, 694, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18

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(2744, 757, F27, 18) (dual of [757, 713, 19]-code) [i](u, u+v)-Construction
2Linear OA(2745, 767, F27, 18) (dual of [767, 722, 19]-code) [i]
3Linear OA(2746, 777, F27, 18) (dual of [777, 731, 19]-code) [i]
4Linear OA(2747, 781, F27, 18) (dual of [781, 734, 19]-code) [i]
5Linear OA(2748, 793, F27, 18) (dual of [793, 745, 19]-code) [i]
6Linear OA(2749, 797, F27, 18) (dual of [797, 748, 19]-code) [i]
7Linear OA(2750, 834, F27, 18) (dual of [834, 784, 19]-code) [i]
8Linear OA(2750, 745, F27, 18) (dual of [745, 695, 19]-code) [i]Generalized (u, u+v)-Construction
9Linear OA(2749, 744, F27, 18) (dual of [744, 695, 19]-code) [i]
10Linear OA(2748, 743, F27, 18) (dual of [743, 695, 19]-code) [i](u, u−v, u+v+w)-Construction
11Linear OA(2749, 745, F27, 18) (dual of [745, 696, 19]-code) [i]
12Linear OA(2750, 785, F27, 18) (dual of [785, 735, 19]-code) [i]
13Linear OA(2737, 731, F27, 19) (dual of [731, 694, 20]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
14Linear OA(2735, 731, F27, 18) (dual of [731, 696, 19]-code) [i]✔
15Linear OA(2740, 734, F27, 20) (dual of [734, 694, 21]-code) [i]✔
16Linear OA(2736, 734, F27, 18) (dual of [734, 698, 19]-code) [i]✔
17Linear OA(2743, 737, F27, 21) (dual of [737, 694, 22]-code) [i]✔
18Linear OA(2737, 737, F27, 18) (dual of [737, 700, 19]-code) [i]✔
19Linear OA(2746, 740, F27, 22) (dual of [740, 694, 23]-code) [i]✔
20Linear OA(2738, 740, F27, 18) (dual of [740, 702, 19]-code) [i]✔
21Linear OA(2749, 743, F27, 23) (dual of [743, 694, 24]-code) [i]✔
22Linear OA(2739, 743, F27, 18) (dual of [743, 704, 19]-code) [i]✔
23Linear OA(2752, 746, F27, 24) (dual of [746, 694, 25]-code) [i]✔
24Linear OA(2740, 746, F27, 18) (dual of [746, 706, 19]-code) [i]✔
25Linear OA(2755, 749, F27, 25) (dual of [749, 694, 26]-code) [i]✔
26Linear OA(2741, 749, F27, 18) (dual of [749, 708, 19]-code) [i]✔
27Linear OA(2758, 752, F27, 26) (dual of [752, 694, 27]-code) [i]✔
28Linear OA(2742, 752, F27, 18) (dual of [752, 710, 19]-code) [i]✔
29Linear OA(2762, 756, F27, 28) (dual of [756, 694, 29]-code) [i]✔
30Linear OA(2743, 755, F27, 18) (dual of [755, 712, 19]-code) [i]✔
31Linear OA(2764, 757, F27, 29) (dual of [757, 693, 30]-code) [i]✔
32Linear OA(2765, 759, F27, 29) (dual of [759, 694, 30]-code) [i]✔
33Linear OA(2768, 762, F27, 30) (dual of [762, 694, 31]-code) [i]✔
34Linear OA(2771, 765, F27, 31) (dual of [765, 694, 32]-code) [i]✔
35Linear OA(2774, 767, F27, 32) (dual of [767, 693, 33]-code) [i]✔
36Linear OA(2775, 769, F27, 32) (dual of [769, 694, 33]-code) [i]✔
37Linear OA(2778, 772, F27, 33) (dual of [772, 694, 34]-code) [i]✔
38Linear OA(2781, 775, F27, 34) (dual of [775, 694, 35]-code) [i]✔
39Linear OA(2784, 777, F27, 35) (dual of [777, 693, 36]-code) [i]✔
40Linear OA(2785, 779, F27, 35) (dual of [779, 694, 36]-code) [i]✔
41Linear OA(2788, 781, F27, 36) (dual of [781, 693, 37]-code) [i]✔
42Linear OA(2789, 783, F27, 36) (dual of [783, 694, 37]-code) [i]✔
43Linear OA(2763, 758, F27, 28) (dual of [758, 695, 29]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes