Information on Result #684605
Linear OA(786, 117663, F7, 17) (dual of [117663, 117577, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,7]) based on
- linear OA(785, 117650, F7, 17) (dual of [117650, 117565, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(773, 117650, F7, 15) (dual of [117650, 117577, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(71, 13, F7, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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, 117664, F7, 17) (dual of [117664, 117577, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(788, 117665, F7, 17) (dual of [117665, 117577, 18]-code) | [i] | ||
| 3 | Linear OOA(786, 65833, F7, 2, 17) (dual of [(65833, 2), 131580, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(786, 65833, F7, 3, 17) (dual of [(65833, 3), 197413, 18]-NRT-code) | [i] | ||
| 5 | Digital (69, 86, 65833)-net over F7 | [i] | ||
| 6 | Linear OA(788, 117666, F7, 17) (dual of [117666, 117578, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(786, 58831, F7, 2, 17) (dual of [(58831, 2), 117576, 18]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(786, 39221, F7, 3, 17) (dual of [(39221, 3), 117577, 18]-NRT-code) | [i] | ||
| 9 | Linear OOA(786, 14707, F7, 17, 17) (dual of [(14707, 17), 249933, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |