Information on Result #877435
Linear OOA(8174, 3289, F81, 2, 35) (dual of [(3289, 2), 6504, 36]-NRT-code), using OOA 2-folding based on linear OA(8174, 6578, F81, 35) (dual of [6578, 6504, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(8174, 6579, F81, 35) (dual of [6579, 6505, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,14]) [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(8157, 6562, F81, 29) (dual of [6562, 6505, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(815, 17, F81, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- construction X applied to C([0,17]) ⊂ C([0,14]) [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(8174, 3132, F81, 3, 35) (dual of [(3132, 3), 9322, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8174, 3132, F81, 4, 35) (dual of [(3132, 4), 12454, 36]-NRT-code) | [i] | ||
| 3 | Digital (39, 74, 3132)-net over F81 | [i] | ||