Information on Result #1463607
Linear OOA(8120, 6395, F81, 2, 9) (dual of [(6395, 2), 12770, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8120, 6395, F81, 9) (dual of [6395, 6375, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8120, 6573, F81, 9) (dual of [6573, 6553, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,2]) [i] 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
- construction X applied to C([0,4]) ⊂ C([0,2]) [i] based on
Mode: 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, 3197, F81, 3, 9) (dual of [(3197, 3), 9571, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8120, 3197, F81, 4, 9) (dual of [(3197, 4), 12768, 10]-NRT-code) | [i] | ||