Information on Result #684680
Linear OA(780, 117686, F7, 15) (dual of [117686, 117606, 16]-code), using construction X applied to Ce(14) ⊂ Ce(8) based on
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(743, 117649, F7, 9) (dual of [117649, 117606, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(781, 117687, F7, 15) (dual of [117687, 117606, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(782, 117688, F7, 15) (dual of [117688, 117606, 16]-code) | [i] | ||
| 3 | Linear OA(783, 117689, F7, 15) (dual of [117689, 117606, 16]-code) | [i] | ||
| 4 | Linear OA(779, 117685, F7, 14) (dual of [117685, 117606, 15]-code) | [i] | Truncation | |
| 5 | Linear OOA(780, 117686, F7, 2, 15) (dual of [(117686, 2), 235292, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(780, 117686, F7, 3, 15) (dual of [(117686, 3), 352978, 16]-NRT-code) | [i] | ||
| 7 | Digital (65, 80, 117686)-net over F7 | [i] | ||
| 8 | Linear OA(781, 117688, F7, 15) (dual of [117688, 117607, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(782, 117690, F7, 15) (dual of [117690, 117608, 16]-code) | [i] | ||
| 10 | Linear OA(783, 117692, F7, 15) (dual of [117692, 117609, 16]-code) | [i] | ||
| 11 | Linear OOA(780, 58843, F7, 2, 15) (dual of [(58843, 2), 117606, 16]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(780, 39228, F7, 3, 15) (dual of [(39228, 3), 117604, 16]-NRT-code) | [i] | ||
| 13 | Linear OOA(780, 16812, F7, 15, 15) (dual of [(16812, 15), 252100, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |