Information on Result #877433
Linear OOA(8172, 3286, F81, 2, 35) (dual of [(3286, 2), 6500, 36]-NRT-code), using OOA 2-folding based on linear OA(8172, 6572, F81, 35) (dual of [6572, 6500, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(8172, 6573, F81, 35) (dual of [6573, 6501, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,15]) [i] based on
- linear OA(8169, 6562, F81, 35) (dual of [6562, 6493, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(8161, 6562, F81, 31) (dual of [6562, 6501, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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([0,17]) ⊂ C([0,15]) [i] based on
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(8172, 2376, F81, 3, 35) (dual of [(2376, 3), 7056, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8172, 2376, F81, 4, 35) (dual of [(2376, 4), 9432, 36]-NRT-code) | [i] | ||
| 3 | Digital (37, 72, 2376)-net over F81 | [i] | ||