Information on Result #614467

Linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, 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(796, 16818, F7, 20) (dual of [16818, 16722, 21]-code) [i](u, u+v)-Construction
2Linear OA(797, 16820, F7, 20) (dual of [16820, 16723, 21]-code) [i]
3Linear OA(798, 16822, F7, 20) (dual of [16822, 16724, 21]-code) [i]
4Linear OA(799, 16824, F7, 20) (dual of [16824, 16725, 21]-code) [i]
5Linear OA(7100, 16837, F7, 20) (dual of [16837, 16737, 21]-code) [i]
6Linear OA(7102, 16856, F7, 20) (dual of [16856, 16754, 21]-code) [i]
7Linear OOA(786, 12312, F7, 2, 20) (dual of [(12312, 2), 24538, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
8Linear OOA(786, 12312, F7, 3, 20) (dual of [(12312, 3), 36850, 21]-NRT-code) [i]
9Digital (66, 86, 12312)-net over F7 [i]
10Linear OA(799, 16821, F7, 20) (dual of [16821, 16722, 21]-code) [i](u, u−v, u+v+w)-Construction
11Linear OA(7100, 16823, F7, 20) (dual of [16823, 16723, 21]-code) [i]
12Linear OA(7102, 16826, F7, 20) (dual of [16826, 16724, 21]-code) [i]
13Linear OA(792, 16813, F7, 22) (dual of [16813, 16721, 23]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
14Linear OA(786, 16812, F7, 20) (dual of [16812, 16726, 21]-code) [i]✔
15Linear OA(798, 16815, F7, 23) (dual of [16815, 16717, 24]-code) [i]✔
16Linear OA(799, 16820, F7, 23) (dual of [16820, 16721, 24]-code) [i]✔
17Linear OA(787, 16818, F7, 20) (dual of [16818, 16731, 21]-code) [i]✔
18Linear OA(7105, 16826, F7, 24) (dual of [16826, 16721, 25]-code) [i]✔
19Linear OA(789, 16825, F7, 20) (dual of [16825, 16736, 21]-code) [i]✔
20Linear OA(790, 16831, F7, 20) (dual of [16831, 16741, 21]-code) [i]✔
21Linear OA(792, 16838, F7, 20) (dual of [16838, 16746, 21]-code) [i]✔
22Linear OA(797, 16848, F7, 20) (dual of [16848, 16751, 21]-code) [i]✔
23Linear OA(798, 16854, F7, 20) (dual of [16854, 16756, 21]-code) [i]✔
24Linear OA(799, 16856, F7, 20) (dual of [16856, 16757, 21]-code) [i]✔
25Linear OA(7102, 16863, F7, 20) (dual of [16863, 16761, 21]-code) [i]✔
26Linear OA(7100, 16859, F7, 20) (dual of [16859, 16759, 21]-code) [i]✔
27Linear OA(7101, 16862, F7, 20) (dual of [16862, 16761, 21]-code) [i]✔
28Linear OA(7104, 16821, F7, 24) (dual of [16821, 16717, 25]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
29Linear OA(7106, 16828, F7, 24) (dual of [16828, 16722, 25]-code) [i]✔
30Linear OA(788, 16820, F7, 20) (dual of [16820, 16732, 21]-code) [i]✔
31Linear OA(791, 16833, F7, 20) (dual of [16833, 16742, 21]-code) [i]✔