Information on Result #614884

Linear OA(856, 32768, F8, 13) (dual of [32768, 32712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13

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(862, 32777, F8, 13) (dual of [32777, 32715, 14]-code) [i](u, u+v)-Construction
2Linear OA(863, 32782, F8, 13) (dual of [32782, 32719, 14]-code) [i]
3Linear OA(864, 32785, F8, 13) (dual of [32785, 32721, 14]-code) [i]
4Linear OA(865, 32792, F8, 13) (dual of [32792, 32727, 14]-code) [i]
5Linear OA(866, 32794, F8, 13) (dual of [32794, 32728, 14]-code) [i]
6Linear OOA(856, 22975, F8, 2, 13) (dual of [(22975, 2), 45894, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
7Linear OOA(856, 22975, F8, 3, 13) (dual of [(22975, 3), 68869, 14]-NRT-code) [i]
8Digital (43, 56, 22975)-net over F8 [i]
9Linear OA(865, 32778, F8, 13) (dual of [32778, 32713, 14]-code) [i](u, u−v, u+v+w)-Construction
10Linear OA(866, 32786, F8, 13) (dual of [32786, 32720, 14]-code) [i]
11Linear OA(861, 32773, F8, 14) (dual of [32773, 32712, 15]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
12Linear OA(856, 32773, F8, 13) (dual of [32773, 32717, 14]-code) [i]✔
13Linear OA(867, 32779, F8, 15) (dual of [32779, 32712, 16]-code) [i]✔
14Linear OA(857, 32779, F8, 13) (dual of [32779, 32722, 14]-code) [i]✔
15Linear OA(875, 32787, F8, 17) (dual of [32787, 32712, 18]-code) [i]✔
16Linear OA(859, 32786, F8, 13) (dual of [32786, 32727, 14]-code) [i]✔
17Linear OA(882, 32794, F8, 18) (dual of [32794, 32712, 19]-code) [i]✔
18Linear OA(860, 32792, F8, 13) (dual of [32792, 32732, 14]-code) [i]✔
19Linear OA(888, 32800, F8, 19) (dual of [32800, 32712, 20]-code) [i]✔
20Linear OA(863, 32800, F8, 13) (dual of [32800, 32737, 14]-code) [i]✔
21Linear OA(897, 32809, F8, 20) (dual of [32809, 32712, 21]-code) [i]✔
22Linear OA(8104, 32816, F8, 21) (dual of [32816, 32712, 22]-code) [i]✔
23Linear OA(8110, 32822, F8, 22) (dual of [32822, 32712, 23]-code) [i]✔
24Linear OA(8116, 32828, F8, 23) (dual of [32828, 32712, 24]-code) [i]✔
25Linear OA(8124, 32832, F8, 25) (dual of [32832, 32708, 26]-code) [i]✔
26Linear OA(8122, 32833, F8, 24) (dual of [32833, 32711, 25]-code) [i]✔
27Linear OA(896, 32807, F8, 20) (dual of [32807, 32711, 21]-code) [i]✔
28Linear OA(866, 32807, F8, 13) (dual of [32807, 32741, 14]-code) [i]✔
29Linear OA(8124, 32834, F8, 25) (dual of [32834, 32710, 26]-code) [i]✔
30Linear OA(8125, 32836, F8, 25) (dual of [32836, 32711, 26]-code) [i]✔
31Linear OA(8126, 32838, F8, 25) (dual of [32838, 32712, 26]-code) [i]✔
32Linear OA(8124, 32836, F8, 24) (dual of [32836, 32712, 25]-code) [i]✔
33Linear OA(881, 32789, F8, 18) (dual of [32789, 32708, 19]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
34Linear OA(873, 32781, F8, 16) (dual of [32781, 32708, 17]-code) [i]✔
35Linear OA(876, 32789, F8, 17) (dual of [32789, 32713, 18]-code) [i]✔
36Linear OA(868, 32781, F8, 15) (dual of [32781, 32713, 16]-code) [i]✔
37Linear OA(858, 32781, F8, 13) (dual of [32781, 32723, 14]-code) [i]✔
38Linear OA(862, 32795, F8, 13) (dual of [32795, 32733, 14]-code) [i]✔
39Linear OA(872, 32785, F8, 15) (dual of [32785, 32713, 16]-code) [i]✔Construction X4 with Extended Narrow-Sense BCH Codes
40Linear OA(857, 32785, F8, 12) (dual of [32785, 32728, 13]-code) [i]✔