Information on Result #614906

Linear OA(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15

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(873, 32778, F8, 15) (dual of [32778, 32705, 16]-code) [i](u, u+v)-Construction
2Linear OA(874, 32782, F8, 15) (dual of [32782, 32708, 16]-code) [i]
3Linear OA(875, 32785, F8, 15) (dual of [32785, 32710, 16]-code) [i]
4Linear OA(876, 32792, F8, 15) (dual of [32792, 32716, 16]-code) [i]
5Linear OA(877, 32795, F8, 15) (dual of [32795, 32718, 16]-code) [i]
6Linear OA(878, 32797, F8, 15) (dual of [32797, 32719, 16]-code) [i]
7Linear OA(877, 32780, F8, 15) (dual of [32780, 32703, 16]-code) [i]Generalized (u, u+v)-Construction
8Linear OOA(866, 26524, F8, 2, 15) (dual of [(26524, 2), 52982, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
9Linear OOA(866, 26524, F8, 3, 15) (dual of [(26524, 3), 79506, 16]-NRT-code) [i]
10Digital (51, 66, 26524)-net over F8 [i]
11Linear OA(878, 32787, F8, 15) (dual of [32787, 32709, 16]-code) [i](u, u−v, u+v+w)-Construction
12Linear OA(872, 32774, F8, 17) (dual of [32774, 32702, 18]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
13Linear OA(866, 32773, F8, 15) (dual of [32773, 32707, 16]-code) [i]✔
14Linear OA(878, 32777, F8, 18) (dual of [32777, 32699, 19]-code) [i]✔
15Linear OA(879, 32781, F8, 18) (dual of [32781, 32702, 19]-code) [i]✔
16Linear OA(867, 32779, F8, 15) (dual of [32779, 32712, 16]-code) [i]✔
17Linear OA(885, 32787, F8, 19) (dual of [32787, 32702, 20]-code) [i]✔
18Linear OA(869, 32786, F8, 15) (dual of [32786, 32717, 16]-code) [i]✔
19Linear OA(892, 32794, F8, 20) (dual of [32794, 32702, 21]-code) [i]✔
20Linear OA(870, 32792, F8, 15) (dual of [32792, 32722, 16]-code) [i]✔
21Linear OA(898, 32800, F8, 21) (dual of [32800, 32702, 22]-code) [i]✔
22Linear OA(872, 32799, F8, 15) (dual of [32799, 32727, 16]-code) [i]✔
23Linear OA(8107, 32809, F8, 22) (dual of [32809, 32702, 23]-code) [i]✔
24Linear OA(873, 32805, F8, 15) (dual of [32805, 32732, 16]-code) [i]✔
25Linear OA(8114, 32816, F8, 23) (dual of [32816, 32702, 24]-code) [i]✔
26Linear OA(8121, 32823, F8, 25) (dual of [32823, 32702, 26]-code) [i]✔
27Linear OA(8127, 32829, F8, 26) (dual of [32829, 32702, 27]-code) [i]✔
28Linear OA(8134, 32832, F8, 27) (dual of [32832, 32698, 28]-code) [i]✔
29Linear OA(8138, 32840, F8, 27) (dual of [32840, 32702, 28]-code) [i]✔
30Linear OA(8106, 32807, F8, 22) (dual of [32807, 32701, 23]-code) [i]✔
31Linear OA(8134, 32834, F8, 27) (dual of [32834, 32700, 28]-code) [i]✔
32Linear OA(8135, 32836, F8, 27) (dual of [32836, 32701, 28]-code) [i]✔
33Linear OA(8136, 32838, F8, 27) (dual of [32838, 32702, 28]-code) [i]✔
34Linear OA(891, 32789, F8, 20) (dual of [32789, 32698, 21]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
35Linear OA(886, 32789, F8, 19) (dual of [32789, 32703, 20]-code) [i]✔
36Linear OA(868, 32781, F8, 15) (dual of [32781, 32713, 16]-code) [i]✔
37Linear OA(871, 32794, F8, 15) (dual of [32794, 32723, 16]-code) [i]✔
38Linear OA(867, 32785, F8, 14) (dual of [32785, 32718, 15]-code) [i]✔Construction X4 with Extended Narrow-Sense BCH Codes
39Linear OOA(866, 4681, F8, 15, 15) (dual of [(4681, 15), 70149, 16]-NRT-code) [i]OOA Folding and Stacking with Additional Row