Information on Result #614336

Linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12

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(757, 16815, F7, 12) (dual of [16815, 16758, 13]-code) [i](u, u+v)-Construction
2Linear OA(758, 16817, F7, 12) (dual of [16817, 16759, 13]-code) [i]
3Linear OA(759, 16825, F7, 12) (dual of [16825, 16766, 13]-code) [i]
4Linear OOA(751, 12680, F7, 2, 12) (dual of [(12680, 2), 25309, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(751, 12680, F7, 3, 12) (dual of [(12680, 3), 37989, 13]-NRT-code) [i]
6Digital (39, 51, 12680)-net over F7 [i]
7Linear OA(760, 16817, F7, 12) (dual of [16817, 16757, 13]-code) [i](u, u−v, u+v+w)-Construction
8Linear OA(756, 16812, F7, 13) (dual of [16812, 16756, 14]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
9Linear OA(751, 16812, F7, 12) (dual of [16812, 16761, 13]-code) [i]✔
10Linear OA(762, 16818, F7, 14) (dual of [16818, 16756, 15]-code) [i]✔
11Linear OA(763, 16815, F7, 15) (dual of [16815, 16752, 16]-code) [i]✔
12Linear OA(764, 16820, F7, 15) (dual of [16820, 16756, 16]-code) [i]✔
13Linear OA(752, 16818, F7, 12) (dual of [16818, 16766, 13]-code) [i]✔
14Linear OA(770, 16826, F7, 16) (dual of [16826, 16756, 17]-code) [i]✔
15Linear OA(754, 16825, F7, 12) (dual of [16825, 16771, 13]-code) [i]✔
16Linear OA(777, 16833, F7, 17) (dual of [16833, 16756, 18]-code) [i]✔
17Linear OA(755, 16831, F7, 12) (dual of [16831, 16776, 13]-code) [i]✔
18Linear OA(783, 16839, F7, 18) (dual of [16839, 16756, 19]-code) [i]✔
19Linear OA(758, 16839, F7, 12) (dual of [16839, 16781, 13]-code) [i]✔
20Linear OA(792, 16848, F7, 19) (dual of [16848, 16756, 20]-code) [i]✔
21Linear OA(798, 16854, F7, 20) (dual of [16854, 16756, 21]-code) [i]✔
22Linear OA(7104, 16856, F7, 21) (dual of [16856, 16752, 22]-code) [i]✔
23Linear OA(7107, 16863, F7, 21) (dual of [16863, 16756, 22]-code) [i]✔
24Linear OA(7105, 16857, F7, 22) (dual of [16857, 16752, 23]-code) [i]✔
25Linear OA(7107, 16861, F7, 22) (dual of [16861, 16754, 23]-code) [i]✔
26Linear OA(7108, 16864, F7, 22) (dual of [16864, 16756, 23]-code) [i]✔
27Linear OA(7105, 16859, F7, 21) (dual of [16859, 16754, 22]-code) [i]✔
28Linear OA(7106, 16862, F7, 21) (dual of [16862, 16756, 22]-code) [i]✔
29Linear OA(776, 16828, F7, 17) (dual of [16828, 16752, 18]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
30Linear OA(771, 16828, F7, 16) (dual of [16828, 16757, 17]-code) [i]✔
31Linear OA(763, 16820, F7, 14) (dual of [16820, 16757, 15]-code) [i]✔
32Linear OA(753, 16820, F7, 12) (dual of [16820, 16767, 13]-code) [i]✔
33Linear OA(757, 16834, F7, 12) (dual of [16834, 16777, 13]-code) [i]✔