Information on Result #699319
Linear OA(8140, 6573, F81, 19) (dual of [6573, 6533, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8129, 6562, F81, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-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 OA(980, 13146, F9, 19) (dual of [13146, 13066, 20]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8140, 3286, F81, 2, 19) (dual of [(3286, 2), 6532, 20]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8140, 2191, F81, 3, 19) (dual of [(2191, 3), 6533, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(8140, 1643, F81, 4, 19) (dual of [(1643, 4), 6532, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(8140, 730, F81, 19, 19) (dual of [(730, 19), 13830, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |