Information on Result #684679
Linear OA(786, 117686, F7, 16) (dual of [117686, 117600, 17]-code), using construction X applied to Ce(15) ⊂ Ce(9) based on
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(787, 117687, F7, 16) (dual of [117687, 117600, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(788, 117688, F7, 16) (dual of [117688, 117600, 17]-code) | [i] | ||
| 3 | Linear OA(789, 117689, F7, 16) (dual of [117689, 117600, 17]-code) | [i] | ||
| 4 | Linear OOA(786, 117686, F7, 2, 16) (dual of [(117686, 2), 235286, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(786, 117686, F7, 3, 16) (dual of [(117686, 3), 352972, 17]-NRT-code) | [i] | ||
| 6 | Digital (70, 86, 117686)-net over F7 | [i] | ||
| 7 | Linear OA(787, 117688, F7, 16) (dual of [117688, 117601, 17]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(788, 117690, F7, 16) (dual of [117690, 117602, 17]-code) | [i] | ||
| 9 | Linear OA(789, 117692, F7, 16) (dual of [117692, 117603, 17]-code) | [i] | ||
| 10 | Linear OOA(786, 58843, F7, 2, 16) (dual of [(58843, 2), 117600, 17]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(786, 39228, F7, 3, 16) (dual of [(39228, 3), 117598, 17]-NRT-code) | [i] | ||
| 12 | Linear OOA(786, 14710, F7, 16, 16) (dual of [(14710, 16), 235274, 17]-NRT-code) | [i] | OA Folding and Stacking | |