Information on Result #877517
Linear OOA(8179, 3290, F81, 2, 37) (dual of [(3290, 2), 6501, 38]-NRT-code), using OOA 2-folding based on linear OA(8179, 6580, F81, 37) (dual of [6580, 6501, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(8179, 6581, F81, 37) (dual of [6581, 6502, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(29) [i] based on
- linear OA(8173, 6561, F81, 37) (dual of [6561, 6488, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- construction X applied to Ce(36) ⊂ Ce(29) [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(8179, 3290, F81, 3, 37) (dual of [(3290, 3), 9791, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8179, 3290, F81, 4, 37) (dual of [(3290, 4), 13081, 38]-NRT-code) | [i] | ||
| 3 | Digital (42, 79, 3290)-net over F81 | [i] | ||