Information on Result #877476
Linear OOA(8176, 3289, F81, 2, 36) (dual of [(3289, 2), 6502, 37]-NRT-code), using OOA 2-folding based on linear OA(8176, 6578, F81, 36) (dual of [6578, 6502, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- linear OA(8171, 6561, F81, 36) (dual of [6561, 6490, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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
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(8176, 3117, F81, 3, 36) (dual of [(3117, 3), 9275, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8176, 3117, F81, 4, 36) (dual of [(3117, 4), 12392, 37]-NRT-code) | [i] | ||
| 3 | Digital (40, 76, 3117)-net over F81 | [i] | ||