Information on Result #617829

Linear OA(2780, 729, F27, 42) (dual of [729, 649, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42

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(27101, 757, F27, 42) (dual of [757, 656, 43]-code) [i](u, u+v)-Construction
2Linear OA(27102, 767, F27, 42) (dual of [767, 665, 43]-code) [i]
3Linear OA(27103, 777, F27, 42) (dual of [777, 674, 43]-code) [i]
4Linear OA(27104, 781, F27, 42) (dual of [781, 677, 43]-code) [i]
5Linear OA(27105, 793, F27, 42) (dual of [793, 688, 43]-code) [i]
6Linear OA(27106, 797, F27, 42) (dual of [797, 691, 43]-code) [i]
7Linear OA(27107, 805, F27, 42) (dual of [805, 698, 43]-code) [i]
8Linear OA(27108, 811, F27, 42) (dual of [811, 703, 43]-code) [i]
9Linear OA(27109, 813, F27, 42) (dual of [813, 704, 43]-code) [i]
10Linear OA(27110, 817, F27, 42) (dual of [817, 707, 43]-code) [i]
11Linear OA(27109, 759, F27, 42) (dual of [759, 650, 43]-code) [i](u, u−v, u+v+w)-Construction
12Linear OA(27110, 761, F27, 42) (dual of [761, 651, 43]-code) [i]
13Linear OA(2782, 731, F27, 43) (dual of [731, 649, 44]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
14Linear OA(2780, 731, F27, 42) (dual of [731, 651, 43]-code) [i]✔
15Linear OA(2785, 734, F27, 44) (dual of [734, 649, 45]-code) [i]✔
16Linear OA(2781, 734, F27, 42) (dual of [734, 653, 43]-code) [i]✔
17Linear OA(2788, 737, F27, 45) (dual of [737, 649, 46]-code) [i]✔
18Linear OA(2782, 737, F27, 42) (dual of [737, 655, 43]-code) [i]✔
19Linear OA(2791, 740, F27, 46) (dual of [740, 649, 47]-code) [i]✔
20Linear OA(2783, 740, F27, 42) (dual of [740, 657, 43]-code) [i]✔
21Linear OA(2794, 743, F27, 47) (dual of [743, 649, 48]-code) [i]✔
22Linear OA(2784, 743, F27, 42) (dual of [743, 659, 43]-code) [i]✔
23Linear OA(2797, 746, F27, 48) (dual of [746, 649, 49]-code) [i]✔
24Linear OA(2785, 746, F27, 42) (dual of [746, 661, 43]-code) [i]✔
25Linear OA(27100, 749, F27, 49) (dual of [749, 649, 50]-code) [i]✔
26Linear OA(2786, 749, F27, 42) (dual of [749, 663, 43]-code) [i]✔
27Linear OA(27103, 752, F27, 50) (dual of [752, 649, 51]-code) [i]✔
28Linear OA(2787, 752, F27, 42) (dual of [752, 665, 43]-code) [i]✔
29Linear OA(27106, 755, F27, 51) (dual of [755, 649, 52]-code) [i]✔
30Linear OA(2788, 755, F27, 42) (dual of [755, 667, 43]-code) [i]✔
31Linear OA(27109, 757, F27, 52) (dual of [757, 648, 53]-code) [i]✔
32Linear OA(27110, 759, F27, 52) (dual of [759, 649, 53]-code) [i]✔
33Linear OA(2789, 757, F27, 42) (dual of [757, 668, 43]-code) [i]✔
34Linear OA(2790, 759, F27, 42) (dual of [759, 669, 43]-code) [i]✔
35Linear OA(2791, 762, F27, 42) (dual of [762, 671, 43]-code) [i]✔
36Linear OA(2792, 765, F27, 42) (dual of [765, 673, 43]-code) [i]✔
37Linear OA(2793, 767, F27, 42) (dual of [767, 674, 43]-code) [i]✔
38Linear OA(2794, 769, F27, 42) (dual of [769, 675, 43]-code) [i]✔
39Linear OA(2795, 771, F27, 42) (dual of [771, 676, 43]-code) [i]✔
40Linear OA(2797, 775, F27, 42) (dual of [775, 678, 43]-code) [i]✔
41Linear OA(2798, 777, F27, 42) (dual of [777, 679, 43]-code) [i]✔
42Linear OA(2799, 779, F27, 42) (dual of [779, 680, 43]-code) [i]✔
43Linear OA(27100, 781, F27, 42) (dual of [781, 681, 43]-code) [i]✔
44Linear OA(27101, 783, F27, 42) (dual of [783, 682, 43]-code) [i]✔
45Linear OA(27102, 786, F27, 42) (dual of [786, 684, 43]-code) [i]✔
46Linear OA(27103, 789, F27, 42) (dual of [789, 686, 43]-code) [i]✔
47Linear OA(27104, 792, F27, 42) (dual of [792, 688, 43]-code) [i]✔