Information on Result #617565

Linear OA(2739, 729, F27, 20) (dual of [729, 690, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20

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(2749, 757, F27, 20) (dual of [757, 708, 21]-code) [i](u, u+v)-Construction
2Linear OA(2750, 767, F27, 20) (dual of [767, 717, 21]-code) [i]
3Linear OA(2751, 777, F27, 20) (dual of [777, 726, 21]-code) [i]
4Linear OA(2752, 781, F27, 20) (dual of [781, 729, 21]-code) [i]
5Linear OA(2753, 793, F27, 20) (dual of [793, 740, 21]-code) [i]
6Linear OA(2754, 797, F27, 20) (dual of [797, 743, 21]-code) [i]
7Linear OA(2755, 805, F27, 20) (dual of [805, 750, 21]-code) [i]
8Linear OA(2756, 834, F27, 20) (dual of [834, 778, 21]-code) [i]
9Linear OA(2756, 747, F27, 20) (dual of [747, 691, 21]-code) [i]Generalized (u, u+v)-Construction
10Linear OA(2752, 743, F27, 20) (dual of [743, 691, 21]-code) [i](u, u−v, u+v+w)-Construction
11Linear OA(2753, 745, F27, 20) (dual of [745, 692, 21]-code) [i]
12Linear OA(2754, 747, F27, 20) (dual of [747, 693, 21]-code) [i]
13Linear OA(2755, 785, F27, 20) (dual of [785, 730, 21]-code) [i]
14Linear OA(2756, 795, F27, 20) (dual of [795, 739, 21]-code) [i]
15Linear OA(2741, 731, F27, 21) (dual of [731, 690, 22]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
16Linear OA(2739, 731, F27, 20) (dual of [731, 692, 21]-code) [i]✔
17Linear OA(2744, 734, F27, 22) (dual of [734, 690, 23]-code) [i]✔
18Linear OA(2740, 734, F27, 20) (dual of [734, 694, 21]-code) [i]✔
19Linear OA(2747, 737, F27, 23) (dual of [737, 690, 24]-code) [i]✔
20Linear OA(2741, 737, F27, 20) (dual of [737, 696, 21]-code) [i]✔
21Linear OA(2750, 740, F27, 24) (dual of [740, 690, 25]-code) [i]✔
22Linear OA(2742, 740, F27, 20) (dual of [740, 698, 21]-code) [i]✔
23Linear OA(2753, 743, F27, 25) (dual of [743, 690, 26]-code) [i]✔
24Linear OA(2743, 743, F27, 20) (dual of [743, 700, 21]-code) [i]✔
25Linear OA(2756, 746, F27, 26) (dual of [746, 690, 27]-code) [i]✔
26Linear OA(2744, 746, F27, 20) (dual of [746, 702, 21]-code) [i]✔
27Linear OA(2760, 750, F27, 28) (dual of [750, 690, 29]-code) [i]✔
28Linear OA(2745, 749, F27, 20) (dual of [749, 704, 21]-code) [i]✔
29Linear OA(2762, 752, F27, 29) (dual of [752, 690, 30]-code) [i]✔
30Linear OA(2746, 752, F27, 20) (dual of [752, 706, 21]-code) [i]✔
31Linear OA(2765, 755, F27, 30) (dual of [755, 690, 31]-code) [i]✔
32Linear OA(2747, 755, F27, 20) (dual of [755, 708, 21]-code) [i]✔
33Linear OA(2768, 757, F27, 31) (dual of [757, 689, 32]-code) [i]✔
34Linear OA(2769, 759, F27, 31) (dual of [759, 690, 32]-code) [i]✔
35Linear OA(2748, 757, F27, 20) (dual of [757, 709, 21]-code) [i]✔
36Linear OA(2749, 759, F27, 20) (dual of [759, 710, 21]-code) [i]✔
37Linear OA(2772, 762, F27, 32) (dual of [762, 690, 33]-code) [i]✔
38Linear OA(2775, 765, F27, 33) (dual of [765, 690, 34]-code) [i]✔
39Linear OA(2778, 767, F27, 34) (dual of [767, 689, 35]-code) [i]✔
40Linear OA(2779, 769, F27, 34) (dual of [769, 690, 35]-code) [i]✔
41Linear OA(2782, 772, F27, 35) (dual of [772, 690, 36]-code) [i]✔
42Linear OA(2785, 775, F27, 36) (dual of [775, 690, 37]-code) [i]✔
43Linear OA(2788, 777, F27, 37) (dual of [777, 689, 38]-code) [i]✔
44Linear OA(2789, 779, F27, 37) (dual of [779, 690, 38]-code) [i]✔
45Linear OA(2792, 781, F27, 38) (dual of [781, 689, 39]-code) [i]✔
46Linear OA(2793, 783, F27, 38) (dual of [783, 690, 39]-code) [i]✔
47Linear OA(2796, 786, F27, 39) (dual of [786, 690, 40]-code) [i]✔
48Linear OA(2799, 789, F27, 40) (dual of [789, 690, 41]-code) [i]✔