Information on Result #615057

Linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26

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(8124, 32782, F8, 26) (dual of [32782, 32658, 27]-code) [i](u, u+v)-Construction
2Linear OA(8125, 32784, F8, 26) (dual of [32784, 32659, 27]-code) [i]
3Linear OA(8126, 32786, F8, 26) (dual of [32786, 32660, 27]-code) [i]
4Linear OA(8127, 32792, F8, 26) (dual of [32792, 32665, 27]-code) [i]
5Linear OA(8128, 32795, F8, 26) (dual of [32795, 32667, 27]-code) [i]
6Linear OA(8130, 32799, F8, 26) (dual of [32799, 32669, 27]-code) [i]
7Linear OA(8131, 32802, F8, 26) (dual of [32802, 32671, 27]-code) [i]
8Linear OA(8132, 32805, F8, 26) (dual of [32805, 32673, 27]-code) [i]
9Linear OA(8131, 32789, F8, 26) (dual of [32789, 32658, 27]-code) [i]Generalized (u, u+v)-Construction
10Linear OOA(8111, 19280, F8, 2, 26) (dual of [(19280, 2), 38449, 27]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
11Linear OOA(8111, 19280, F8, 3, 26) (dual of [(19280, 3), 57729, 27]-NRT-code) [i]
12Digital (85, 111, 19280)-net over F8 [i]
13Linear OA(8128, 32786, F8, 26) (dual of [32786, 32658, 27]-code) [i](u, u−v, u+v+w)-Construction
14Linear OA(8131, 32790, F8, 26) (dual of [32790, 32659, 27]-code) [i]
15Linear OA(8132, 32792, F8, 26) (dual of [32792, 32660, 27]-code) [i]
16Linear OA(8116, 32773, F8, 27) (dual of [32773, 32657, 28]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
17Linear OA(8111, 32773, F8, 26) (dual of [32773, 32662, 27]-code) [i]✔
18Linear OA(8122, 32779, F8, 28) (dual of [32779, 32657, 29]-code) [i]✔
19Linear OA(8113, 32777, F8, 26) (dual of [32777, 32664, 27]-code) [i]✔
20Linear OA(8114, 32781, F8, 26) (dual of [32781, 32667, 27]-code) [i]✔
21Linear OA(8129, 32786, F8, 29) (dual of [32786, 32657, 30]-code) [i]✔
22Linear OA(8115, 32787, F8, 26) (dual of [32787, 32672, 27]-code) [i]✔
23Linear OA(8135, 32792, F8, 30) (dual of [32792, 32657, 31]-code) [i]✔
24Linear OA(8117, 32794, F8, 26) (dual of [32794, 32677, 27]-code) [i]✔
25Linear OA(8142, 32799, F8, 31) (dual of [32799, 32657, 32]-code) [i]✔
26Linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code) [i]✔
27Linear OA(8152, 32809, F8, 33) (dual of [32809, 32657, 34]-code) [i]✔
28Linear OA(8148, 32805, F8, 32) (dual of [32805, 32657, 33]-code) [i]✔
29Linear OA(8122, 32809, F8, 26) (dual of [32809, 32687, 27]-code) [i]✔
30Linear OA(8159, 32816, F8, 34) (dual of [32816, 32657, 35]-code) [i]✔
31Linear OA(8124, 32816, F8, 26) (dual of [32816, 32692, 27]-code) [i]✔
32Linear OA(8165, 32822, F8, 35) (dual of [32822, 32657, 36]-code) [i]✔
33Linear OA(8125, 32822, F8, 26) (dual of [32822, 32697, 27]-code) [i]✔
34Linear OA(8171, 32828, F8, 36) (dual of [32828, 32657, 37]-code) [i]✔
35Linear OA(8127, 32829, F8, 26) (dual of [32829, 32702, 27]-code) [i]✔
36Linear OA(8129, 32832, F8, 26) (dual of [32832, 32703, 27]-code) [i]✔
37Linear OA(8151, 32807, F8, 33) (dual of [32807, 32656, 34]-code) [i]✔
38Linear OA(8121, 32807, F8, 26) (dual of [32807, 32686, 27]-code) [i]✔
39Linear OA(8129, 32834, F8, 26) (dual of [32834, 32705, 27]-code) [i]✔
40Linear OA(8130, 32836, F8, 26) (dual of [32836, 32706, 27]-code) [i]✔
41Linear OA(8131, 32838, F8, 26) (dual of [32838, 32707, 27]-code) [i]✔
42Linear OA(8141, 32794, F8, 31) (dual of [32794, 32653, 32]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
43Linear OA(8136, 32794, F8, 30) (dual of [32794, 32658, 31]-code) [i]✔
44Linear OA(8128, 32781, F8, 29) (dual of [32781, 32653, 30]-code) [i]✔
45Linear OA(8123, 32781, F8, 28) (dual of [32781, 32658, 29]-code) [i]✔
46Linear OA(8116, 32789, F8, 26) (dual of [32789, 32673, 27]-code) [i]✔