Information on Result #699324
Linear OA(8120, 6573, F81, 9) (dual of [6573, 6553, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,2]) based on
- linear OA(8117, 6562, F81, 9) (dual of [6562, 6545, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(819, 6562, F81, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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 OOA(8120, 6395, F81, 2, 9) (dual of [(6395, 2), 12770, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8120, 6395, F81, 3, 9) (dual of [(6395, 3), 19165, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(8120, 6395, F81, 4, 9) (dual of [(6395, 4), 25560, 10]-NRT-code) | [i] | ||
| 4 | Digital (11, 20, 6395)-net over F81 | [i] | ||
| 5 | Linear OOA(8120, 3286, F81, 2, 9) (dual of [(3286, 2), 6552, 10]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8120, 2191, F81, 3, 9) (dual of [(2191, 3), 6553, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(8120, 1643, F81, 4, 9) (dual of [(1643, 4), 6552, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(8120, 1643, F81, 9, 9) (dual of [(1643, 9), 14767, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |