Information on Result #699128
Linear OA(8146, 531457, F81, 15) (dual of [531457, 531411, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,5]) based on
- linear OA(8143, 531442, F81, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(8131, 531442, F81, 11) (dual of [531442, 531411, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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 OOA(8146, 286155, F81, 2, 15) (dual of [(286155, 2), 572264, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8146, 286155, F81, 3, 15) (dual of [(286155, 3), 858419, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(8146, 286155, F81, 4, 15) (dual of [(286155, 4), 1144574, 16]-NRT-code) | [i] | ||
| 4 | Digital (31, 46, 286155)-net over F81 | [i] | ||
| 5 | Linear OOA(8146, 265728, F81, 2, 15) (dual of [(265728, 2), 531410, 16]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8146, 177152, F81, 3, 15) (dual of [(177152, 3), 531410, 16]-NRT-code) | [i] | ||
| 7 | Linear OOA(8146, 132864, F81, 4, 15) (dual of [(132864, 4), 531410, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(8146, 75922, F81, 15, 15) (dual of [(75922, 15), 1138784, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |